Cheyanne Leigh

2021-02-21

In this question, the function f is differentiable, and f'(x) = g(x). We don't know exactly what f(x) or g(x) are, so your answers will have f(x) and g(x) in them.

Compute the derivatives of the following function.

$e}^{\mathrm{sin}\left(f\left(x\right)\right)$

Compute the derivatives of the following function.

Raheem Donnelly

Skilled2021-02-23Added 75 answers

Use chain rule to compute the derivatives.

$\frac{d}{dx}\left({e}^{\mathrm{sin}\left(f\left(x\right)\right)}\right)=\frac{d}{d\left(\mathrm{sin}\left(f\left(x\right)\right)\right)}\left({e}^{\mathrm{sin}\left(f\left(x\right)\right)}\right)\times \frac{d}{d\left(f\left(x\right)\right)}\left(\mathrm{sin}\left(f\left(x\right)\right)\right)\times \frac{d}{dx}f\left(x\right)$

$={e}^{\mathrm{sin}\left(f\left(x\right)\right)}\times \mathrm{cos}\left(f\left(x\right)\right)\times {f}^{\prime}\left(x\right)$

$={e}^{\mathrm{sin}\left(f\left(x\right)\right)}\times \mathrm{cos}\left(f\left(x\right)\right)\times g\left(x\right)$

$={e}^{\mathrm{sin}\left(f\left(x\right)\right)}g\left(x\right)\mathrm{cos}\left(f\left(x\right)\right)$

Jeffrey Jordon

Expert2022-01-31Added 2575 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-01-31Added 2575 answers

Answer is given below (on video)