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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{\frac{4}{3}}, g = (2 - x)^{3}

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

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

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

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

Simplify

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

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

\int \frac{49 - x ^{2}}{x ^{4}} d x

\frac{d ^{3}}{d x ^{3}} (x^{6} e^{x})

f (x) = \frac{6 x + 5}{x - 1}, at x = 2

t \to 2 lim (\frac{t - 2}{t ^{2} - 4})

\int 19 tan^{2} (x) sec^{3} (x) d x

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