What is (\partial)/(\partial x)(ln(4-x^2)) ?

The answer to (\partial)/(\partial x)(ln(4-x^2)) is -(2x)/(4-x^2)

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(\partial)/(\partial x)(ln(4-x^2))

\frac{\partial}{\partial x} (ln (4 - x^{2}))

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

Solution steps

\frac{\partial}{\partial x} (ln (4 - x^{2}))

Apply the chain rule:

\frac{1}{4 - x ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

= \frac{1}{4 - x ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

\frac{\partial}{\partial x} (4 - x^{2}) = - 2 x

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

Simplify

\frac{1}{4 - x ^{2}} (- 2 x) : - \frac{2 x}{4 - x ^{2}}

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

y = 4 x^{2} - x^{3}, (1, 3)

(0.1) (1.1)

x \to a lim (0)

f (x) = x x + 3

\int \frac{5 x}{x} d x

What is (\partial)/(\partial x)(ln(4-x^2)) ?
The answer to (\partial)/(\partial x)(ln(4-x^2)) is -(2x)/(4-x^2)