# 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 $$e^{\sin{x^2}}\cdot \cos{x^2}\cdot 2x$$

Share:
1,252 Author by

Adarsh is interested in learning technologies that will help him build a personal autonomous vehicle.

Updated on January 10, 2023

• 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

• • 1) $e$ stands for a particular constant. 2) Do you know how to use the chain rule? You need to apply it twice here.
• The title says "function of $y$" instead of $x$.
• (Audit?) You have already solved (differentiated) $y$ with respect to $x$ assuming constant $e$ to be the Napierian base using Chain Rule.