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zi2lalZ

Answered question

2021-10-11

Derivatives Find the derivative of the following functions.

y = \ln 2 x^{8}

saiyansruleA

Skilled2021-10-12Added 110 answers

Step 1:To determine
Given:

y = \ln (2 x^{8})

To determine:
Find the derivative of the given function.
Step 2:Formula used

\frac{d}{d x} (\ln x) = \frac{1}{x}

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

Step 3:Calculation
Consider the given function

y = \ln (2 x^{8})

Differentiating with respect to x and applying chain rule, we get,

\frac{d y}{d x} = \frac{d}{d x} (\ln (2 x^{8}))

\Rightarrow \frac{d y}{d x} = \frac{1}{2 x^{8}} \cdot \frac{d}{d x} (2 x^{8})

\Rightarrow \frac{d y}{d x} = \frac{1}{2 x^{8}} \cdot (2 (8) x^{7})

\Rightarrow \frac{d y}{d x} = \frac{1}{2 x^{8}} \cdot 16 x^{7}

\Rightarrow \frac{d y}{d x} = \frac{8}{x}

Hence,

\frac{d y}{d x} = \frac{8}{x}

Jeffrey Jordon

Expert2022-11-15Added 2605 answers

Answer is given below (on video)

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