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Popular >

derivative of ln(sqrt(4+x^2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{4 + x ^{2}} \cdot \frac{x}{4 + x ^{2}}

Simplify

\frac{1}{4 + x ^{2}} \cdot \frac{x}{4 + x ^{2}} : \frac{x}{4 + x ^{2}}

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

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Frequently Asked Questions (FAQ)

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