What is the derivative of (x^2(x+1)^{1/3}) ?

The derivative of (x^2(x+1)^{1/3}) is (7x^2+6x)/(3(x+1)^{2/3)}

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

The first derivative of (x^2(x+1)^{1/3}) is (7x^2+6x)/(3(x+1)^{2/3)}

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = (x + 1)^{\frac{1}{3}}

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

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

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

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

Simplify

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

= \frac{7 x ^{2} + 6 x}{3 ( x + 1 ) ^{\frac{2}{3}}}

\int_{0}^{\frac{π}{4}} sin^{4} (2 x) d x

\frac{5}{x ^{4}}

\frac{2 x}{5 - cot ( x )}

\frac{d}{d x} (ln^{2} (5 x))

(x, y) \to (2, 3) lim (x + y^{2})

What is the derivative of (x^2(x+1)^{1/3}) ?
The derivative of (x^2(x+1)^{1/3}) is (7x^2+6x)/(3(x+1)^{2/3)}
What is the first derivative of (x^2(x+1)^{1/3}) ?
The first derivative of (x^2(x+1)^{1/3}) is (7x^2+6x)/(3(x+1)^{2/3)}