What is the derivative of f(x)=x^{7/5}(x+5) ?

The derivative of f(x)=x^{7/5}(x+5) is (12x^{7/5}+35x^{2/5})/5

What is the first derivative of f(x)=x^{7/5}(x+5) ?

The first derivative of f(x)=x^{7/5}(x+5) is (12x^{7/5}+35x^{2/5})/5

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derivative of

f (x) = x^{\frac{7}{5}} (x + 5)

\frac{12 x ^{\frac{7}{5}} + 35 x ^{\frac{2}{5}}}{5}

Solution steps

\frac{d}{d x} (x^{\frac{7}{5}} (x + 5))

Apply the Product Rule:

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

f = x^{\frac{7}{5}}, g = x + 5

= \frac{d}{d x} (x^{\frac{7}{5}}) (x + 5) + \frac{d}{d x} (x + 5) x^{\frac{7}{5}}

\frac{d}{d x} (x^{\frac{7}{5}}) = \frac{7 x ^{\frac{2}{5}}}{5}

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

= \frac{7 x ^{\frac{2}{5}}}{5} (x + 5) + 1 \cdot x^{\frac{7}{5}}

Simplify

\frac{7 x ^{\frac{2}{5}}}{5} (x + 5) + 1 \cdot x^{\frac{7}{5}} : \frac{12 x ^{\frac{7}{5}} + 35 x ^{\frac{2}{5}}}{5}

= \frac{12 x ^{\frac{7}{5}} + 35 x ^{\frac{2}{5}}}{5}

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What is the derivative of f(x)=x^{7/5}(x+5) ?
The derivative of f(x)=x^{7/5}(x+5) is (12x^{7/5}+35x^{2/5})/5
What is the first derivative of f(x)=x^{7/5}(x+5) ?
The first derivative of f(x)=x^{7/5}(x+5) is (12x^{7/5}+35x^{2/5})/5