Find the derivative of the following function
1,252
Use the chain rule, $$(f(g(x))'=f'(g(x))g'(x)$$
For three functions, $$(f(g(h(x))))'=f'(g(h(x)))g'(h(x))h'(x)$$
Set $f(x) = e^x, g(x) = \sin{x}, h(x)=x^2$ to arrive at the desired answer.
Calculations: $f'(x)=e^x, g'(x)=\cos{x}, h'(x)=2x$, thus, the result is $$e^{\sin{x^2}}\cdot \cos{x^2}\cdot 2x$$
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Adarsh TS
Adarsh is interested in learning technologies that will help him build a personal autonomous vehicle.
Updated on January 10, 2023Comments

Adarsh TS 10 months
Given function:
$$f(x) = e^{\sin(x^2)}$$
Find the derivative of the above function where '$e$' stands for some constant.
I assume the correct answer is $e^{\sin(x^2)}\cdot \cos(x^2)\cdot 2x$, which method is best to solve like a question this?? Please help out to resolve this problem

MathAdam over 5 yearse stands for "some constant"? Your solution assumes e is Euler's constant. How did you get your solution? Why do you "assume" that is the correct answer?

angryavian over 5 years1) $e$ stands for a particular constant. 2) Do you know how to use the chain rule? You need to apply it twice here.

mr_e_man over 5 yearsThe title says "function of $y$" instead of $x$.

Narasimham over 5 years(Audit?) You have already solved (differentiated) $y$ with respect to $x$ assuming constant $e$ to be the Napierian base using Chain Rule.
