Key to "Derivatives Find and simplify the derivative of the..."

Burhan Hopper

Answered question

2021-10-14

Derivatives Find and simplify the derivative of the following functions

f (x) = 3 x^{- 9}

liingliing8

Skilled2021-10-15Added 95 answers

Step 1: Given that:

f (x) = 3 x^{- 9}

We need to find the derivative and simplify the given function.
Step 2: Derivative
We have,

f (x) = 3 x^{- 9}

Differentiating both sides w.r.t. x we get,

\frac{d}{d x} (f^{'} (x)) = \frac{d}{d x} (3 x^{- 9})

Using the power rule,

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

We have,

f^{'} (x) = 3 (- 9 x^{- 9 - 1})

\Rightarrow f^{'} (x) = 3 (- 9 x^{- 10})

\Rightarrow f^{'} (x) = - 27 x^{- 10}

\Rightarrow f^{'} (x) = - \frac{27}{x^{10}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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