What is the derivative of ln((x^2^2)) ?

The derivative of ln((x^2^2)) is 4/x

What is the first derivative of ln((x^2^2)) ?

The first derivative of ln((x^2^2)) is 4/x

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\frac{d}{d x} (ln ((x^{2})^{2}))

\frac{4}{x}

Solution steps

\frac{d}{d x} (ln ((x^{2})^{2}))

Simplify

ln ((x^{2})^{2}) : ln (x^{4})

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

Apply the chain rule:

\frac{1}{x ^{4}} \frac{d}{d x} (x^{4})

= \frac{1}{x ^{4}} \frac{d}{d x} (x^{4})

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

= \frac{1}{x ^{4}} \cdot 4 x^{3}

Simplify

\frac{1}{x ^{4}} \cdot 4 x^{3} : \frac{4}{x}

= \frac{4}{x}

(- π, 0), (- \frac{π}{2}, 4)

\frac{2}{y}

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

\frac{\partial}{\partial x} (\frac{7 x - 5 y}{y ^{2} + 2 x ^{2}})

\frac{d}{d y} (3 x^{2} y)

What is the derivative of ln((x^2^2)) ?
The derivative of ln((x^2^2)) is 4/x
What is the first derivative of ln((x^2^2)) ?
The first derivative of ln((x^2^2)) is 4/x