Solve ( ln^(2) (1 x^(4)))'

Evaluate

((ln (1 \times x^{4}))^{2})^{'}

Any expression multiplied by 1 remains the same

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

Rewrite the expression

\frac{d}{d x} ((ln (x^{4}))^{2})

Use the chain rule \frac{d}{d x} (f (g)) = \frac{d}{d g} (f (g)) \times \frac{d}{d x} (g) where the g = ln (x^{4}), to find the derivative

\frac{d}{d g} (g^{2}) \times \frac{d}{d x} (ln (x^{4}))

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

2 g \times \frac{d}{d x} (ln (x^{4}))

Calculate

More Steps

2 g \times \frac{4}{x}

Substitute back

2 ln (x^{4}) \times \frac{4}{x}

Multiply the terms

\frac{2 ln ( x ^{4} ) \times 4}{x}

Multiply the terms

\frac{8 ln ( x ^{4} )}{x}

Use ln b^{n} = n ln b to simplify the expression

\frac{8 \times 4 ln ( x )}{x}

Solution

\frac{32 ln ( x )}{x}

Evaluate the derivative