What is the derivative of ln^4(x) ?

The derivative of ln^4(x) is (4ln^3(x))/x

What is the first derivative of ln^4(x) ?

The first derivative of ln^4(x) is (4ln^3(x))/x

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\frac{d}{d x} (ln^{4} (x))

\frac{4 ln ^{3} ( x )}{x}

Solution steps

\frac{d}{d x} (ln^{4} (x))

Apply the chain rule:

4 (ln (x))^{3} \frac{d}{d x} (ln (x))

= 4 (ln (x))^{3} \frac{d}{d x} (ln (x))

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

= 4 (ln (x))^{3} \frac{1}{x}

Simplify

4 ln^{3} (x) \frac{1}{x} : \frac{4 ln ^{3} ( x )}{x}

= \frac{4 ln ^{3} ( x )}{x}

\frac{s + 2}{s ( s + 1 ) ^{2}}

g (t) = 2 t^{- \frac{3}{4}}

\frac{\partial}{\partial x} (e^{x} + yz)

3 x y^{^{'}} - y (x + 1) + 7 y^{4} = 0

\frac{d y}{d x}, x^{2} + y^{2} = 24

What is the derivative of ln^4(x) ?
The derivative of ln^4(x) is (4ln^3(x))/x
What is the first derivative of ln^4(x) ?
The first derivative of ln^4(x) is (4ln^3(x))/x