What is the derivative of (x^3-8^{2/3}) ?

The derivative of (x^3-8^{2/3}) is (2x^2)/((x^3-8)^{1/3)}

What is the first derivative of (x^3-8^{2/3}) ?

The first derivative of (x^3-8^{2/3}) is (2x^2)/((x^3-8)^{1/3)}

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\frac{d}{d x} ((x^{3} - 8)^{\frac{2}{3}})

\frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x^{3} - 8)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} - 8)

= \frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} - 8)

\frac{d}{d x} (x^{3} - 8) = 3 x^{2}

= \frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \cdot 3 x^{2}

Simplify

\frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \cdot 3 x^{2} : \frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

= \frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

x \to 3 - lim (x^{2} - 8)

\frac{\partial}{\partial x} (- e^{x} cos (y))

\int csc^{2} (5 t) d t

y = \frac{3}{x}, y = 12 x, y = \frac{x}{3}

y^{^{'}} + 5 y = e^{(- 2 x)}

What is the derivative of (x^3-8^{2/3}) ?
The derivative of (x^3-8^{2/3}) is (2x^2)/((x^3-8)^{1/3)}
What is the first derivative of (x^3-8^{2/3}) ?
The first derivative of (x^3-8^{2/3}) is (2x^2)/((x^3-8)^{1/3)}