What is the derivative of ln(x^7) ?

The derivative of ln(x^7) is 7/x

What is the first derivative of ln(x^7) ?

The first derivative of ln(x^7) is 7/x

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derivative of

ln (x^{7})

\frac{7}{x}

Solution steps

\frac{d}{d x} (ln (x^{7}))

Apply the chain rule:

\frac{1}{x ^{7}} \frac{d}{d x} (x^{7})

= \frac{1}{x ^{7}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{1}{x ^{7}} \cdot 7 x^{6}

Simplify

\frac{1}{x ^{7}} \cdot 7 x^{6} : \frac{7}{x}

= \frac{7}{x}

\int_{0}^{4} x^{3} d x

\int - (x - 3)^{2} d x

\frac{d}{d x} (y^{2} - 2 y cos (x))

y = 10 x^{4} - 10 x^{2}, y = 9 x^{2}

\int 1 + (cos (x))^{2} d x

What is the derivative of ln(x^7) ?
The derivative of ln(x^7) is 7/x
What is the first derivative of ln(x^7) ?
The first derivative of ln(x^7) is 7/x