What is the derivative of y=x^{2/5}(x+3) ?

The derivative of y=x^{2/5}(x+3) is (7x+6)/(5x^{3/5)}

What is the first derivative of y=x^{2/5}(x+3) ?

The first derivative of y=x^{2/5}(x+3) is (7x+6)/(5x^{3/5)}

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derivative of

y = x^{\frac{2}{5}} (x + 3)

\frac{7 x + 6}{5 x ^{\frac{3}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{2}{5}} (x + 3))

Apply the Product Rule:

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

f = x^{\frac{2}{5}}, g = x + 3

= \frac{d}{d x} (x^{\frac{2}{5}}) (x + 3) + \frac{d}{d x} (x + 3) x^{\frac{2}{5}}

\frac{d}{d x} (x^{\frac{2}{5}}) = \frac{2}{5 x ^{\frac{3}{5}}}

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

= \frac{2}{5 x ^{\frac{3}{5}}} (x + 3) + 1 \cdot x^{\frac{2}{5}}

Simplify

\frac{2}{5 x ^{\frac{3}{5}}} (x + 3) + 1 \cdot x^{\frac{2}{5}} : \frac{7 x + 6}{5 x ^{\frac{3}{5}}}

= \frac{7 x + 6}{5 x ^{\frac{3}{5}}}

\frac{d}{d x} (\frac{x ^{3} - 4}{x - 1})

\int \frac{3 x - 2}{x + 1} d x

x \to - 3 lim (∣ - x - 1 ∣)

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

d er i v a t i v e \frac{6}{5} - \frac{6}{5} e^{- 20 t}

What is the derivative of y=x^{2/5}(x+3) ?
The derivative of y=x^{2/5}(x+3) is (7x+6)/(5x^{3/5)}
What is the first derivative of y=x^{2/5}(x+3) ?
The first derivative of y=x^{2/5}(x+3) is (7x+6)/(5x^{3/5)}