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

The derivative of (ln(x)^7) is (7ln^6(x))/x

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

The first derivative of (ln(x)^7) is (7ln^6(x))/x

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

\frac{7 ln ^{6} ( x )}{x}

Solution steps

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

Apply the chain rule:

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

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

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

= 7 (ln (x))^{6} \frac{1}{x}

Simplify

7 ln^{6} (x) \frac{1}{x} : \frac{7 ln ^{6} ( x )}{x}

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

\frac{\partial}{\partial x} (6 x^{2} e^{y} - 7 x y^{3})

\int \frac{( 1 + cot ^{2} ( z ) ) cot ( z )}{csc ( z )} d z

\int z e^{y} d y

\frac{d y}{d t} = 1 + t + y + t y

\frac{d}{d x} (x^{2} + 2 x - 8)

What is the derivative of (ln(x)^7) ?
The derivative of (ln(x)^7) is (7ln^6(x))/x
What is the first derivative of (ln(x)^7) ?
The first derivative of (ln(x)^7) is (7ln^6(x))/x