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Popular >

derivative of ln(1-5x^2+x^3)

Solution

\frac{d}{d x} (ln (1 - 5 x^{2} + x^{3}))

Solution

\frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}

Solution steps

\frac{d}{d x} (ln (1 - 5 x^{2} + x^{3}))

Apply the chain rule:

\frac{1}{1 - 5 x ^{2} + x ^{3}} \frac{d}{d x} (1 - 5 x^{2} + x^{3})

= \frac{1}{1 - 5 x ^{2} + x ^{3}} \frac{d}{d x} (1 - 5 x^{2} + x^{3})

\frac{d}{d x} (1 - 5 x^{2} + x^{3}) = 3 x^{2} - 10 x

= \frac{1}{1 - 5 x ^{2} + x ^{3}} (3 x^{2} - 10 x)

Simplify

\frac{1}{1 - 5 x ^{2} + x ^{3}} (3 x^{2} - 10 x) : \frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}

= \frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(1-5x^2+x^3) ?
The derivative of ln(1-5x^2+x^3) is (3x^2-10x)/(1-5x^2+x^3)
What is the first derivative of ln(1-5x^2+x^3) ?
The first derivative of ln(1-5x^2+x^3) is (3x^2-10x)/(1-5x^2+x^3)