What is the derivative of x^{4/5}(x-4^2) ?

The derivative of x^{4/5}(x-4^2) is (14x^2-72x+64)/(5x^{1/5)}

What is the first derivative of x^{4/5}(x-4^2) ?

The first derivative of x^{4/5}(x-4^2) is (14x^2-72x+64)/(5x^{1/5)}

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\frac{d}{d x} (x^{\frac{4}{5}} (x - 4)^{2})

\frac{14 x ^{2} - 72 x + 64}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{5}} (x - 4)^{2})

Apply the Product Rule:

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

f = x^{\frac{4}{5}}, g = (x - 4)^{2}

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 4)^{2} + \frac{d}{d x} ((x - 4)^{2}) x^{\frac{4}{5}}

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

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

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

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 4)^{2} + 2 (x - 4) x^{\frac{4}{5}} : \frac{14 x ^{2} - 72 x + 64}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 72 x + 64}{5 x ^{\frac{1}{5}}}

x y + y^{2} - x^{2} \frac{d y}{d x} = 0

\int_{1}^{2} 11 4 x^{2} - 3 d x

\frac{1}{( s ^{2} + 1 ) ( s ^{2} - 6 )}

f (x) = (e^{x} + 1)^{7 x}

\frac{4}{s} + \frac{6}{s ^{2}} - \frac{1}{s + 8}

What is the derivative of x^{4/5}(x-4^2) ?
The derivative of x^{4/5}(x-4^2) is (14x^2-72x+64)/(5x^{1/5)}
What is the first derivative of x^{4/5}(x-4^2) ?
The first derivative of x^{4/5}(x-4^2) is (14x^2-72x+64)/(5x^{1/5)}