Solved: "Derivatives involving other trigonometric functions Find the derivative..."

alesterp

Answered question

2021-10-05

Derivatives involving other trigonometric functions Find the derivative of the following functions.

y = e^{5 x} \csc x

Sally Cresswell

Skilled2021-10-06Added 91 answers

Step 1
Given:

y = e^{5 x} \csc x

Determine the derivative using product rule.
Step 2

\frac{d}{d x} (e^{5 x} \csc x) = e^{5 x} (\frac{d}{d x} (\csc x)) + \csc x (\frac{d}{d x} (e^{5 x}))

= e^{5 x} (\csc x \cot x) + 5 e^{5 x} \csc x

= e^{5 x} \csc x (\cot x + 5)

Therefore, the derivative of the function is

e^{5 x} \csc x (\cot x + 5)

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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