What is the derivative of x(x-4^{1/3}) ?

The derivative of x(x-4^{1/3}) is (4x-12)/(3(x-4)^{2/3)}

What is the first derivative of x(x-4^{1/3}) ?

The first derivative of x(x-4^{1/3}) is (4x-12)/(3(x-4)^{2/3)}

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

\frac{4 x - 12}{3 ( x - 4 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 4)^{\frac{1}{3}}

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

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

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

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

Simplify

1 \cdot (x - 4)^{\frac{1}{3}} + \frac{1}{3 ( x - 4 ) ^{\frac{2}{3}}} x : \frac{4 x - 12}{3 ( x - 4 ) ^{\frac{2}{3}}}

= \frac{4 x - 12}{3 ( x - 4 ) ^{\frac{2}{3}}}

\frac{d y}{d t} = 3 t^{2}

\frac{\partial}{\partial x} (x^{7} y^{6} + 4 x^{6} y)

\int 8 x^{\frac{1}{2}} d x

x \to 2 lim (e^{\frac{1}{0}})

y = 3 tan (x), at x = \frac{π}{6}

What is the derivative of x(x-4^{1/3}) ?
The derivative of x(x-4^{1/3}) is (4x-12)/(3(x-4)^{2/3)}
What is the first derivative of x(x-4^{1/3}) ?
The first derivative of x(x-4^{1/3}) is (4x-12)/(3(x-4)^{2/3)}