Best solutions to - "Find the derivative of function defined as follows...." - Plainmath

gonjenjemeb

Answered question

2021-11-22

Find the derivative of function defined as follows.

y = 5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1}

Answer & Explanation

Jeffrey Parrish

Beginner2021-11-23Added 15 answers

Step 1
Given function is:

y = 5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1}

We have to find

\frac{d y}{d x}

.
We will use the following formula for derivatives:

\frac{d}{d x} (x^{n}) = n x^{n - 1}

; n is an integer
Step 2
Then we get,

\frac{d y}{d x} = \frac{d}{d x} (5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1})

\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (5 x^{- 5}) - \frac{d}{d x} (6 x^{- 2}) + \frac{d}{d x} (13 x^{- 1})

\Rightarrow \frac{d y}{d x} = 5 (- 5) x^{- 5 - 1} - 6 (- 2) x^{- 2 - 1} + 13 (- 1) x^{- 1 - 1}

\Rightarrow \frac{d y}{d x} = - 25 x^{- 6} + 12 x^{- 3} - 13 x^{- 2}

\Rightarrow \frac{d y}{d x} = - \frac{25}{x^{6}} + \frac{12}{x^{3}} - \frac{13}{x^{2}}

Hence the answer.

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