What is the derivative of x(2x+7)^{2/3} ?

The derivative of x(2x+7)^{2/3} is (10x+21)/(3(2x+7)^{1/3)}

What is the first derivative of x(2x+7)^{2/3} ?

The first derivative of x(2x+7)^{2/3} is (10x+21)/(3(2x+7)^{1/3)}

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derivative of

x (2 x + 7)^{\frac{2}{3}}

\frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (x (2 x + 7)^{\frac{2}{3}})

Apply the Product Rule:

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

f = x, g = (2 x + 7)^{\frac{2}{3}}

= \frac{d x}{d x} (2 x + 7)^{\frac{2}{3}} + \frac{d}{d x} ((2 x + 7)^{\frac{2}{3}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x + 7)^{\frac{2}{3}}) = \frac{4}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

= 1 \cdot (2 x + 7)^{\frac{2}{3}} + \frac{4}{3 ( 2 x + 7 ) ^{\frac{1}{3}}} x

Simplify

1 \cdot (2 x + 7)^{\frac{2}{3}} + \frac{4}{3 ( 2 x + 7 ) ^{\frac{1}{3}}} x : \frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

= \frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

t \to 2 lim (8 + t^{3})

y = e^{- x} sin (x), y = - e^{- x} sin (x), 0 \leq x \leq π

\int \frac{cos ( 7 x )}{1 + sin ^{2} ( 7 x )} d x

f (x) = x^{2} (x - 2)^{4}

\frac{d y}{d x} = \frac{y}{x ^{2} + 1}

What is the derivative of x(2x+7)^{2/3} ?
The derivative of x(2x+7)^{2/3} is (10x+21)/(3(2x+7)^{1/3)}
What is the first derivative of x(2x+7)^{2/3} ?
The first derivative of x(2x+7)^{2/3} is (10x+21)/(3(2x+7)^{1/3)}