What is the derivative of x^{1/3}(x+8) ?

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

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

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

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

\frac{4 x + 8}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x^{\frac{1}{3}}, g = x + 8

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

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

\frac{d}{d x} (x + 8) = 1

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

Simplify

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

= \frac{4 x + 8}{3 x ^{\frac{2}{3}}}

\frac{\partial}{\partial z} (x yz + x y^{2} + y z^{2} + z x^{2})

\frac{10}{s + 10}

\int \frac{5 x}{( 6 - x ^{2} ) ^{3}} d x

\int_{0}^{3} \frac{x}{x ^{2} + 16} d x

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