What is the derivative of 2x^{1/5}(x^3-8) ?

The derivative of 2x^{1/5}(x^3-8) is (2(16x^3-8))/(5x^{4/5)}

What is the first derivative of 2x^{1/5}(x^3-8) ?

The first derivative of 2x^{1/5}(x^3-8) is (2(16x^3-8))/(5x^{4/5)}

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derivative of

2 x^{\frac{1}{5}} (x^{3} - 8)

\frac{2 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} (2 x^{\frac{1}{5}} (x^{3} - 8))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{\frac{1}{5}} (x^{3} - 8))

Apply the Product Rule:

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

f = x^{\frac{1}{5}}, g = x^{3} - 8

= 2 (\frac{d}{d x} (x^{\frac{1}{5}}) (x^{3} - 8) + \frac{d}{d x} (x^{3} - 8) x^{\frac{1}{5}})

\frac{d}{d x} (x^{\frac{1}{5}}) = \frac{1}{5 x ^{\frac{4}{5}}}

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

= 2 (\frac{1}{5 x ^{\frac{4}{5}}} (x^{3} - 8) + 3 x^{2} x^{\frac{1}{5}})

Simplify

2 (\frac{1}{5 x ^{\frac{4}{5}}} (x^{3} - 8) + 3 x^{2} x^{\frac{1}{5}}) : \frac{2 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

= \frac{2 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

x \to 0 lim (\frac{x}{cos ( x )})

\int t^{2} + t t - 1 + t sin (π) t d t

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

\frac{d}{d x} (\frac{1}{2} x + 3)

\int e^{2 x} - \frac{1}{2} e^{\frac{x}{2}} d x

What is the derivative of 2x^{1/5}(x^3-8) ?
The derivative of 2x^{1/5}(x^3-8) is (2(16x^3-8))/(5x^{4/5)}
What is the first derivative of 2x^{1/5}(x^3-8) ?
The first derivative of 2x^{1/5}(x^3-8) is (2(16x^3-8))/(5x^{4/5)}