Check the solution to "Find the derivative of the following functions y=e−xsin⁡x" - Plainmath

Cem Hayes

Answered question

2021-10-22

Find the derivative of the following functions

y = e^{- x} \sin x

Answer & Explanation

Aubree Mcintyre

Skilled2021-10-23Added 73 answers

Step 1 Let us find the derivative of given function
Given:

y = e^{- x} \sin x

Product rule:

\frac{d}{d x} (u v) = u v^{'} + v u^{'}

Step 2

u = 4^{- x} v = \sin x

u^{'} = - 4^{- x} \ln (4) v^{'} = \cos x

y^{'} = (4^{- x}) \cos x - \sin x (4^{- x} \ln (4))

y^{'} = 4^{- x} \cos x - 4^{- x} \sin x \ln (4)

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