What is the derivative of ln(5-x^2) ?

The derivative of ln(5-x^2) is -(2x)/(5-x^2)

What is the first derivative of ln(5-x^2) ?

The first derivative of ln(5-x^2) is -(2x)/(5-x^2)

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\frac{d}{d x} (ln (5 - x^{2}))

- \frac{2 x}{5 - x ^{2}}

Solution steps

\frac{d}{d x} (ln (5 - x^{2}))

Apply the chain rule:

\frac{1}{5 - x ^{2}} \frac{d}{d x} (5 - x^{2})

= \frac{1}{5 - x ^{2}} \frac{d}{d x} (5 - x^{2})

\frac{d}{d x} (5 - x^{2}) = - 2 x

= \frac{1}{5 - x ^{2}} (- 2 x)

Simplify

\frac{1}{5 - x ^{2}} (- 2 x) : - \frac{2 x}{5 - x ^{2}}

= - \frac{2 x}{5 - x ^{2}}

\int_{2}^{4} \frac{1}{16 - t ^{2}} d t

x \to 2 lim (2 x - 2)

\int \frac{x ^{3}}{x ^{2} - 2 x + 4} d x

\int \frac{sec ( x )}{x} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = - 3 t e^{- t}

What is the derivative of ln(5-x^2) ?
The derivative of ln(5-x^2) is -(2x)/(5-x^2)
What is the first derivative of ln(5-x^2) ?
The first derivative of ln(5-x^2) is -(2x)/(5-x^2)