What is the derivative of y=x^{4/5}(x-3) ?

The derivative of y=x^{4/5}(x-3) is (9x-12)/(5x^{1/5)}

What is the first derivative of y=x^{4/5}(x-3) ?

The first derivative of y=x^{4/5}(x-3) is (9x-12)/(5x^{1/5)}

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derivative of

y = x^{\frac{4}{5}} (x - 3)

\frac{9 x - 12}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{5}} (x - 3))

Apply the Product Rule:

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

f = x^{\frac{4}{5}}, g = x - 3

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 3) + \frac{d}{d x} (x - 3) x^{\frac{4}{5}}

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

\frac{d}{d x} (x - 3) = 1

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

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 3) + 1 \cdot x^{\frac{4}{5}} : \frac{9 x - 12}{5 x ^{\frac{1}{5}}}

= \frac{9 x - 12}{5 x ^{\frac{1}{5}}}

\frac{d}{d x} (\frac{- 2 x ^{2} + 25}{25 - x ^{2}})

\frac{d}{d θ} (cos^{2} (θ) - sin^{2} (θ))

\frac{d}{d t} (8 t e^{- t})

\int cos (\frac{y}{x}) d x

n = 0 \sum \infty (- \frac{1}{3})^{n}

What is the derivative of y=x^{4/5}(x-3) ?
The derivative of y=x^{4/5}(x-3) is (9x-12)/(5x^{1/5)}
What is the first derivative of y=x^{4/5}(x-3) ?
The first derivative of y=x^{4/5}(x-3) is (9x-12)/(5x^{1/5)}