What is the derivative of ln^6(x) ?

The derivative of ln^6(x) is (6ln^5(x))/x

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

The first derivative of ln^6(x) is (6ln^5(x))/x

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

\frac{6 ln ^{5} ( x )}{x}

Solution steps

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

Apply the chain rule:

6 (ln (x))^{5} \frac{d}{d x} (ln (x))

= 6 (ln (x))^{5} \frac{d}{d x} (ln (x))

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

= 6 (ln (x))^{5} \frac{1}{x}

Simplify

6 ln^{5} (x) \frac{1}{x} : \frac{6 ln ^{5} ( x )}{x}

= \frac{6 ln ^{5} ( x )}{x}

θ sin (θ)

\frac{d y}{d x} + 7 y - 2 e^{- x} = 0

\frac{d}{d x} (5 arcsin (x^{3}))

x y^{^{'}} - 2 y = 2 x^{2} ln (x)

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

What is the derivative of ln^6(x) ?
The derivative of ln^6(x) is (6ln^5(x))/x
What is the first derivative of ln^6(x) ?
The first derivative of ln^6(x) is (6ln^5(x))/x