What is the derivative of f(x)=6x^{1/5}(x^3-8) ?

The derivative of f(x)=6x^{1/5}(x^3-8) is (6(16x^3-8))/(5x^{4/5)}

What is the first derivative of f(x)=6x^{1/5}(x^3-8) ?

The first derivative of f(x)=6x^{1/5}(x^3-8) is (6(16x^3-8))/(5x^{4/5)}

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derivative of

f (x) = 6 x^{\frac{1}{5}} (x^{3} - 8)

\frac{6 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} (6 x^{\frac{1}{5}} (x^{3} - 8))

Take the constant out:

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

= 6 \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

= 6 (\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}

= 6 (\frac{1}{5 x ^{\frac{4}{5}}} (x^{3} - 8) + 3 x^{2} x^{\frac{1}{5}})

Simplify

6 (\frac{1}{5 x ^{\frac{4}{5}}} (x^{3} - 8) + 3 x^{2} x^{\frac{1}{5}}) : \frac{6 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

= \frac{6 ( 16 x ^{3} - 8 )}{5 x ^{\frac{4}{5}}}

x \to 1 lim (+ \frac{1}{x - 1})

\int e^{θ} cos (θ) d θ

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

\int \frac{1}{e ^{x} - 3} d x

\frac{d}{d x} (ln (cos (x^{2} + 1)))

What is the derivative of f(x)=6x^{1/5}(x^3-8) ?
The derivative of f(x)=6x^{1/5}(x^3-8) is (6(16x^3-8))/(5x^{4/5)}
What is the first derivative of f(x)=6x^{1/5}(x^3-8) ?
The first derivative of f(x)=6x^{1/5}(x^3-8) is (6(16x^3-8))/(5x^{4/5)}