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

The derivative of f(x)=x(x+1)^{1/3} is (4x+3)/(3(x+1)^{2/3)}

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

The first derivative of f(x)=x(x+1)^{1/3} is (4x+3)/(3(x+1)^{2/3)}

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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

(2, 1), (5, 7)

\int \frac{2 e ^{2 x}}{e ^{2 x} + 12 e ^{x} + 35} d x

\frac{d}{d x} (6 - arcsin (\frac{x}{x ^{2} + 4}))

\int (3 x^{2} - 4 x^{3}) d x

What is the derivative of f(x)=x(x+1)^{1/3} ?
The derivative of f(x)=x(x+1)^{1/3} is (4x+3)/(3(x+1)^{2/3)}
What is the first derivative of f(x)=x(x+1)^{1/3} ?
The first derivative of f(x)=x(x+1)^{1/3} is (4x+3)/(3(x+1)^{2/3)}