"Find the derivatives of the functions y=1xsin−5x−x3cos3x" was answered by our experts

Khadija Wells

Answered question

2021-10-12

Find the derivatives of the functions

y = \frac{1}{x} \sin^{- 5} x - \frac{x}{3} \cos^{3} x

stuth1

Skilled2021-10-13Added 97 answers

Step 1
Given function is:

y = \frac{1}{x} \sin^{- 5} x - \frac{x}{3} \cos^{3} x

We have to find

\frac{d y}{d x}

.
Step 2
Then we get,

\frac{d y}{d x} = \frac{d}{d x} (\frac{1}{x} \sin^{- 5} x - \frac{x}{3} \cos^{3} x)

\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (\frac{1}{x} \sin^{- 5} x) - \frac{d}{d x} (\frac{x}{3} \cos^{3} x)

\Rightarrow \frac{d y}{d x} = (- \frac{1}{x^{2}} \sin^{- 5} x - \frac{5}{x} \sin^{- 5 - 1} x \cos x)

- (\frac{1}{3} \cos^{3} x - \frac{x}{3} \cdot 3 \cos^{2} x \sin x)

\Rightarrow \frac{d y}{d x} = - \frac{1}{x^{2}} \sin^{- 5} x - \frac{5}{x} \sin^{- 6} x \cos x - \frac{1}{3} \cos^{3} x + x \cos^{2} x \sin x

Hence the answer.

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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