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Popular >

derivative of ln((x^2+1^{20}))

Solution

\frac{d}{d x} (ln ((x^{2} + 1)^{20}))

Solution

\frac{40 x}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (ln ((x^{2} + 1)^{20}))

Apply the chain rule:

\frac{1}{( x ^{2} + 1 ) ^{20}} \frac{d}{d x} ((x^{2} + 1)^{20})

= \frac{1}{( x ^{2} + 1 ) ^{20}} \frac{d}{d x} ((x^{2} + 1)^{20})

\frac{d}{d x} ((x^{2} + 1)^{20}) = 40 x (x^{2} + 1)^{19}

= \frac{1}{( x ^{2} + 1 ) ^{20}} \cdot 40 x (x^{2} + 1)^{19}

Simplify

\frac{1}{( x ^{2} + 1 ) ^{20}} \cdot 40 x (x^{2} + 1)^{19} : \frac{40 x}{x ^{2} + 1}

= \frac{40 x}{x ^{2} + 1}

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\int_{1}^{2} x^{- 3} d x

t y^{^{'}} + (t + 1) y = t

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\int 6 x (3 x^{2} - 2)^{4} d x

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\int_{0}^{\frac{1}{5}} 4 arcsin (5 y) d y

Frequently Asked Questions (FAQ)

What is the derivative of ln((x^2+1^{20})) ?
The derivative of ln((x^2+1^{20})) is (40x)/(x^2+1)
What is the first derivative of ln((x^2+1^{20})) ?
The first derivative of ln((x^2+1^{20})) is (40x)/(x^2+1)