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Popular Calculus >

derivative of (x^2-4^{2/3})

Solution

\frac{d}{d x} ((x^{2} - 4)^{\frac{2}{3}})

Solution

\frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x^{2} - 4)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 4)

= \frac{2}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = 2 x

= \frac{2}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}} \cdot 2 x

Simplify

\frac{2}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}} \cdot 2 x : \frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

= \frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

Graph

Popular Examples

derivative of sin(bx)

d er i v a t i v e sin (b x)

derivative of 2x-1

d er i v a t i v e 2 x - 1

y^{''}+2y^'=0,y(0)=-4,y^'(0)=2

y^{^{''}} + 2 y^{^{'}} = 0, y (0) = - 4, y^{^{'}} (0) = 2

(\partial)/(\partial x)(x^2*y)

\frac{\partial}{\partial x} (x^{2} \cdot y)

integral of xe^{(2x)}

\int x e^{(2 x)} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-4^{2/3}) ?
The derivative of (x^2-4^{2/3}) is (4x)/(3(x^2-4)^{1/3)}
What is the first derivative of (x^2-4^{2/3}) ?
The first derivative of (x^2-4^{2/3}) is (4x)/(3(x^2-4)^{1/3)}