What is the derivative of y=ln(x^{14}) ?

The derivative of y=ln(x^{14}) is (14)/x

What is the first derivative of y=ln(x^{14}) ?

The first derivative of y=ln(x^{14}) is (14)/x

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derivative of

y = ln (x^{14})

\frac{14}{x}

Solution steps

\frac{d}{d x} (ln (x^{14}))

Apply the chain rule:

\frac{1}{x ^{14}} \frac{d}{d x} (x^{14})

= \frac{1}{x ^{14}} \frac{d}{d x} (x^{14})

\frac{d}{d x} (x^{14}) = 14 x^{13}

= \frac{1}{x ^{14}} \cdot 14 x^{13}

Simplify

\frac{1}{x ^{14}} \cdot 14 x^{13} : \frac{14}{x}

= \frac{14}{x}

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What is the derivative of y=ln(x^{14}) ?
The derivative of y=ln(x^{14}) is (14)/x
What is the first derivative of y=ln(x^{14}) ?
The first derivative of y=ln(x^{14}) is (14)/x