Solution of \left ( \ln{\left ( x^{2} \right )} \right )^{\prime}

Solve ( ln ( x^{2 )} )^prime

Evaluate

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

Rewrite the expression

\frac{d}{d x} (ln (x^{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 = x^{2}, to find the derivative

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

Use \frac{d}{d x} ln x = \frac{1}{x} to find derivative

\frac{1}{g} \times \frac{d}{d x} (x^{2})

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

\frac{1}{g} \times 2 x

Substitute back

\frac{1}{x ^{2}} \times 2 x

Cancel out the common factor x

\frac{1}{x} \times 2

Solution

\frac{2}{x}