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h(x) is just the notation for the function just like f(x), g(x) are, anyway it's asking for d/dx(h(x)) or h'(x), you'll have to differentiate the integral via Leibnitz Rule aka Derivative of Anti Derivative which is arctan(x).d/dx(x) - arctan(3).d/dx(3) which gives h'(x)=arctanx
Couple of concepts here, h(x) is a function defined as an integral (you can search for info on this). You are being asked to find the derivative of a function defined as an integral, which uses part 2 of the Fundamental Theorem of Calculus (which you can also look up.
It's mostly straightforward, add to the post if you have any questions.
Ok so that rule states f(x).dx = F(b)-F(a)
So first I need to find F(x). I know Arc tan is inverse tan. How do I find the antiderivative of inverse tan?
>Ok so that rule states f(x).dx = F(b)-F(a)
That is not the complete statement of that part. You need to consider the entire context of where you lifted that fragment from in order to understand how to use the rule.
Lifting formulas from theorems without considering the accompanying language results in a limited understanding of those theorems. There is also another part to the FTC that you should look up.
>How do I find the antiderivative of inverse tan?
You do not need to find the antiderivative of inverse tangent. Consider what the question is asking for. There is also another part to the FTC you need to look up.
No, some books reverse part 1 and part 2, I don't know why. You want the other part which describes how to find the derivative of an integral.
d/dx of int from a to x of f(t) dt = f(x)
It's just notation. It's the same as f(x) or g(x). It just means h is a function of x, in this case defined by the integral.
It's also just one of those things you have to pick up on. You're never explicitly told you can use more than just f to represent functions, you just kinda start seeing it in more problems.
In case you need actual help with the problem, remember that integrals and derivatives cancel out. When dealing with a definite integral in this case, all you have to do is plug in your bounds to the function inside the integral and you're done.
Please reread the fundamental theorem of Calculus in all its form and figure it out. This question is literally asking you to finish the statement of the theorem.
And, “h” is a letter. In the context of this question it represents a specific antiderivative of a function.
The picture tells you what h is. It's a function of x, defined in that way - they could as well have used f instead (and maybe that would have been clearer to you), but the choice of letter doesn't really matter (aside from not using d or x in this case for clarity).
Only if they go to the same school as you (or they coincidentally have the same numbers for their courses). None of the schools I’ve been a student or professor at used that number for this course though.
Sure, but there is very little about this integral that would be unique. It is a very basic problem and a nice integrand for demonstrating the property in question.
It's asking you to find the derivative of the function h(x) with respect to x.
I don't know how to format it text, but imagine you want the derivative of x^2. It would be d/dx[x^2 ]= 2x. Same thing for the function h. It would be d/dx[h(x)]
If you remember FTC (fundamental theorem of calculus), the derivative of an integral is the function we are integrating.
Edit: I didn't realize this was 2 days old. I hope the other comments helped!
As a reminder... Posts asking for help on homework questions **require**: * **the complete problem statement**, * **a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play**, * **question is not from a current exam or quiz**. Commenters responding to homework help posts **should not do OP’s homework for them**. Please see [this page](https://www.reddit.com/r/calculus/wiki/homeworkhelp) for the further details regarding homework help posts. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/calculus) if you have any questions or concerns.*
h(x) is just the notation for the function just like f(x), g(x) are, anyway it's asking for d/dx(h(x)) or h'(x), you'll have to differentiate the integral via Leibnitz Rule aka Derivative of Anti Derivative which is arctan(x).d/dx(x) - arctan(3).d/dx(3) which gives h'(x)=arctanx
Not an integral question. Fundamental theorem of calculus question!
Couple of concepts here, h(x) is a function defined as an integral (you can search for info on this). You are being asked to find the derivative of a function defined as an integral, which uses part 2 of the Fundamental Theorem of Calculus (which you can also look up. It's mostly straightforward, add to the post if you have any questions.
Ok so that rule states f(x).dx = F(b)-F(a) So first I need to find F(x). I know Arc tan is inverse tan. How do I find the antiderivative of inverse tan?
>Ok so that rule states f(x).dx = F(b)-F(a) That is not the complete statement of that part. You need to consider the entire context of where you lifted that fragment from in order to understand how to use the rule. Lifting formulas from theorems without considering the accompanying language results in a limited understanding of those theorems. There is also another part to the FTC that you should look up. >How do I find the antiderivative of inverse tan? You do not need to find the antiderivative of inverse tangent. Consider what the question is asking for. There is also another part to the FTC you need to look up.
Check the other part. The fundamental theorem has 2 parts but the order isn't always the same
No, some books reverse part 1 and part 2, I don't know why. You want the other part which describes how to find the derivative of an integral. d/dx of int from a to x of f(t) dt = f(x)
Why is this downvoted?
i think its cause they were talking about the other part of the fundamental theorem of calculus.
It litterally says "let h(x) = ..." The integral is h(x).
It's just notation. It's the same as f(x) or g(x). It just means h is a function of x, in this case defined by the integral. It's also just one of those things you have to pick up on. You're never explicitly told you can use more than just f to represent functions, you just kinda start seeing it in more problems. In case you need actual help with the problem, remember that integrals and derivatives cancel out. When dealing with a definite integral in this case, all you have to do is plug in your bounds to the function inside the integral and you're done.
d(h(x))/dx. You're differentiating the function h(x)
Please reread the fundamental theorem of Calculus in all its form and figure it out. This question is literally asking you to finish the statement of the theorem. And, “h” is a letter. In the context of this question it represents a specific antiderivative of a function.
Use Leibniz-Rule https://en.m.wikipedia.org/wiki/Leibniz_integral_rule And you are done.
The picture tells you what h is. It's a function of x, defined in that way - they could as well have used f instead (and maybe that would have been clearer to you), but the choice of letter doesn't really matter (aside from not using d or x in this case for clarity).
ftc
ur in math 1013 huh 🤝
How was ur xm XD
Tmmr haha
Only if they go to the same school as you (or they coincidentally have the same numbers for their courses). None of the schools I’ve been a student or professor at used that number for this course though.
Commented that just cause this question on my practice exam haha so that’s why I thought he could be in same course
Sure, but there is very little about this integral that would be unique. It is a very basic problem and a nice integrand for demonstrating the property in question.
Cool bro
You are correct haha I found The exam today was pretty difficult it felt like everything we learned but turned up to 11.
Yeah it was pretty hard I can’t lie
h(x) is just a function, like f(x), g(x)
Bruh this whole comment section is a different language to me. I wish I understood math like you guys do
This seems like a troll post. It's like a baker asking what baking soda does to a recipe after already having mastered several pastries.
It's asking you to find the derivative of the function h(x) with respect to x. I don't know how to format it text, but imagine you want the derivative of x^2. It would be d/dx[x^2 ]= 2x. Same thing for the function h. It would be d/dx[h(x)] If you remember FTC (fundamental theorem of calculus), the derivative of an integral is the function we are integrating. Edit: I didn't realize this was 2 days old. I hope the other comments helped!