What is the derivative of ln((x^2-x^{13})) ?

The derivative of ln((x^2-x^{13})) is (13(2x-1))/(x^2-x)

What is the first derivative of ln((x^2-x^{13})) ?

The first derivative of ln((x^2-x^{13})) is (13(2x-1))/(x^2-x)

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\frac{d}{d x} (ln ((x^{2} - x)^{13}))

\frac{13 ( 2 x - 1 )}{x ^{2} - x}

Solution steps

\frac{d}{d x} (ln ((x^{2} - x)^{13}))

Apply the chain rule:

\frac{1}{( x ^{2} - x ) ^{13}} \frac{d}{d x} ((x^{2} - x)^{13})

= \frac{1}{( x ^{2} - x ) ^{13}} \frac{d}{d x} ((x^{2} - x)^{13})

\frac{d}{d x} ((x^{2} - x)^{13}) = 13 (x^{2} - x)^{12} (2 x - 1)

= \frac{1}{( x ^{2} - x ) ^{13}} \cdot 13 (x^{2} - x)^{12} (2 x - 1)

Simplify

\frac{1}{( x ^{2} - x ) ^{13}} \cdot 13 (x^{2} - x)^{12} (2 x - 1) : \frac{13 ( 2 x - 1 )}{x ^{2} - x}

= \frac{13 ( 2 x - 1 )}{x ^{2} - x}

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

\int_{0}^{2} 2 x e^{x^{2}} d x

\int \frac{3}{x} + 3 x d x

\frac{\partial}{\partial t} (t e^{t})

x = 4 y, x = y^{2} - 12

What is the derivative of ln((x^2-x^{13})) ?
The derivative of ln((x^2-x^{13})) is (13(2x-1))/(x^2-x)
What is the first derivative of ln((x^2-x^{13})) ?
The first derivative of ln((x^2-x^{13})) is (13(2x-1))/(x^2-x)