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Popular Calculus >

derivative of ln(x^3+6x^2)

Solution

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

Solution

\frac{3 ( x + 4 )}{x ( x + 6 )}

Solution steps

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

Apply the chain rule:

\frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

= \frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

\frac{d}{d x} (x^{3} + 6 x^{2}) = 3 x^{2} + 12 x

= \frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x)

Simplify

\frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x) : \frac{3 ( x + 4 )}{x ( x + 6 )}

= \frac{3 ( x + 4 )}{x ( x + 6 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^3+6x^2) ?
The derivative of ln(x^3+6x^2) is (3(x+4))/(x(x+6))
What is the first derivative of ln(x^3+6x^2) ?
The first derivative of ln(x^3+6x^2) is (3(x+4))/(x(x+6))