What is the derivative of \sqrt[5]{x}(x-1) ?

The derivative of \sqrt[5]{x}(x-1) is (x-1)/(5x^{4/5)}+\sqrt[5]{x}

What is the first derivative of \sqrt[5]{x}(x-1) ?

The first derivative of \sqrt[5]{x}(x-1) is (x-1)/(5x^{4/5)}+\sqrt[5]{x}

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derivative of

5 x (x - 1)

\frac{x - 1}{5 x ^{\frac{4}{5}}} + 5 x

Solution steps

\frac{d}{d x} (5 x (x - 1))

Apply the Product Rule:

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

f = 5 x, g = x - 1

= \frac{d}{d x} (5 x) (x - 1) + \frac{d}{d x} (x - 1) 5 x

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

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

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

Simplify

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

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

\int 2.4

x \to 0 lim (\frac{( ln ( x ) )}{x})

y^{^{''}} - 4 y^{^{'}} + 10 y = 0

sin (4 x)

\frac{\partial}{\partial x} (x^{\frac{4}{7}} y^{\frac{1}{7}} z^{\frac{2}{7}})

What is the derivative of \sqrt[5]{x}(x-1) ?
The derivative of \sqrt[5]{x}(x-1) is (x-1)/(5x^{4/5)}+\sqrt[5]{x}
What is the first derivative of \sqrt[5]{x}(x-1) ?
The first derivative of \sqrt[5]{x}(x-1) is (x-1)/(5x^{4/5)}+\sqrt[5]{x}