Find the derivative of the following function


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


Related videos on Youtube

Adarsh TS
Author by

Adarsh TS

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

Updated on January 10, 2023


  • Adarsh TS
    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
      MathAdam over 5 years
      e 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
      angryavian over 5 years
      1) $e$ 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
      mr_e_man over 5 years
      The title says "function of $y$" instead of $x$.
    • Narasimham
      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.