What is the derivative of x^{4/5}(x-9^2) ?

The derivative of x^{4/5}(x-9^2) is (14x^2-162x+324)/(5x^{1/5)}

What is the first derivative of x^{4/5}(x-9^2) ?

The first derivative of x^{4/5}(x-9^2) is (14x^2-162x+324)/(5x^{1/5)}

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\frac{d}{d x} (x^{\frac{4}{5}} (x - 9)^{2})

\frac{14 x ^{2} - 162 x + 324}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{5}} (x - 9)^{2})

Apply the Product Rule:

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

f = x^{\frac{4}{5}}, g = (x - 9)^{2}

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 9)^{2} + \frac{d}{d x} ((x - 9)^{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 - 9)^{2}) = 2 (x - 9)

= \frac{4}{5 x ^{\frac{1}{5}}} (x - 9)^{2} + 2 (x - 9) x^{\frac{4}{5}}

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 9)^{2} + 2 (x - 9) x^{\frac{4}{5}} : \frac{14 x ^{2} - 162 x + 324}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 162 x + 324}{5 x ^{\frac{1}{5}}}

e^{- x}

x \to 8 lim (\frac{1}{x - 8})

\frac{d}{d x} (\frac{ln ( x )}{4 x})

\frac{6}{x + 4}

x \to - 2 - lim (ln (x + 3))

What is the derivative of x^{4/5}(x-9^2) ?
The derivative of x^{4/5}(x-9^2) is (14x^2-162x+324)/(5x^{1/5)}
What is the first derivative of x^{4/5}(x-9^2) ?
The first derivative of x^{4/5}(x-9^2) is (14x^2-162x+324)/(5x^{1/5)}