differentiate ln(x^2) — step-by-step solution

Let's differentiate:

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

We differentiate using:

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

(where f =

x^{2}

)

ⓘ The derivative of ln(x) is 1/x:

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

\frac{d}{d x} (x^{2}) \cdot \frac{1}{x^{2}}

\frac{d}{d x} (x^{2}) \cdot \frac{1}{x^{2}}

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{d}{d x} (x^{2}) \cdot \frac{1}{x^{2}}

\frac{\frac{d}{d x} (x^{2}) \cdot 1}{x^{2}}

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

■The derivative of x^n is n*x^(n-1):

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

2 x

\frac{2 x}{x^{2}}

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor:

\frac{2 x}{x^{2}}

\frac{2}{x}

▶Derivative:

\frac{2}{x}