What is the derivative of x^{4/5}(x-8^2) ?

The derivative of x^{4/5}(x-8^2) is (14x^2-144x+256)/(5x^{1/5)}

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

The first derivative of x^{4/5}(x-8^2) is (14x^2-144x+256)/(5x^{1/5)}

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

\frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}

Solution steps

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

Apply the Product Rule:

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

f = x^{\frac{4}{5}}, g = (x - 8)^{2}

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

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

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 8)^{2} + 2 (x - 8) x^{\frac{4}{5}} : \frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}

\int_{- 1}^{6} x - 4 x^{2} d x

y^{^{''}} - (\frac{2}{t}) y^{^{'}} + (\frac{2}{t ^{2}}) y = 0

\int (ln (y))^{2} y d y

\frac{x ^{2} + 4}{x ^{2} - 4}

6 - 6 x^{2}, 0

What is the derivative of x^{4/5}(x-8^2) ?
The derivative of x^{4/5}(x-8^2) is (14x^2-144x+256)/(5x^{1/5)}
What is the first derivative of x^{4/5}(x-8^2) ?
The first derivative of x^{4/5}(x-8^2) is (14x^2-144x+256)/(5x^{1/5)}