What is the derivative of f(x)=x^{2/3}(x^2-4) ?

The derivative of f(x)=x^{2/3}(x^2-4) is (8x^2-8)/(3x^{1/3)}

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

The first derivative of f(x)=x^{2/3}(x^2-4) is (8x^2-8)/(3x^{1/3)}

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{2}{3}}, g = x^{2} - 4

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x^{2} - 4) + 2 x x^{\frac{2}{3}} : \frac{8 x ^{2} - 8}{3 x ^{\frac{1}{3}}}

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

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

\frac{d}{d x} (y (θ, x) tan (θ))

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

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

y^{^{'}} + 5 y = e^{- 3 t}

What is the derivative of f(x)=x^{2/3}(x^2-4) ?
The derivative of f(x)=x^{2/3}(x^2-4) is (8x^2-8)/(3x^{1/3)}
What is the first derivative of f(x)=x^{2/3}(x^2-4) ?
The first derivative of f(x)=x^{2/3}(x^2-4) is (8x^2-8)/(3x^{1/3)}