What is the derivative of (x^2-2x-1^{2/3}) ?

The derivative of (x^2-2x-1^{2/3}) is (2(2x-2))/(3(x^2-2x-1)^{1/3)}

What is the first derivative of (x^2-2x-1^{2/3}) ?

The first derivative of (x^2-2x-1^{2/3}) is (2(2x-2))/(3(x^2-2x-1)^{1/3)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int tan^{5} (x) d x

(x + y) e^{\frac{x}{y}} d x + (x - \frac{x ^{2}}{y}) e^{\frac{x}{y}} d y = 0

\int (5 x^{14} - 2 x^{5}) d x

\int (y^{2} - 1)^{2} d y

\frac{d}{d x} (x^{2} + a^{2})

What is the derivative of (x^2-2x-1^{2/3}) ?
The derivative of (x^2-2x-1^{2/3}) is (2(2x-2))/(3(x^2-2x-1)^{1/3)}
What is the first derivative of (x^2-2x-1^{2/3}) ?
The first derivative of (x^2-2x-1^{2/3}) is (2(2x-2))/(3(x^2-2x-1)^{1/3)}