differentiate ln(x^2+4) — step-by-step solution

Let's differentiate:

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

Apply the differentiation rule:

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

with f =

x^{2} + 4

ⓘ Differentiating

\ln (x)

gives

\frac{1}{x}

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

\frac{d}{d x} (x^{2} + 4) \cdot \frac{1}{x^{2} + 4}

\frac{d}{d x} (x^{2} + 4) \cdot \frac{1}{x^{2} + 4}

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{d}{d x} (x^{2} + 4) \cdot \frac{1}{x^{2} + 4}

\frac{\frac{d}{d x} (x^{2} + 4) \cdot 1}{x^{2} + 4}

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

■Differentiate a sum by differentiating each term, then adding the derivatives:

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

\frac{d}{d x} (x^{2}) + 0

\frac{\frac{d}{d x} (x^{2}) + 0}{x^{2} + 4}

ⓘ Adding 0 preserves the original value:

\frac{d}{d x} (x^{2}) + 0

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

■The derivative of

x^{n}

n x^{n - 1}

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

2 x

▶Derivative:

\frac{2 x}{x^{2} + 4}