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

The derivative of (2x^3-12x^{4/3}) is 8(x^2-2)(2x^3-12x)^{1/3}

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

The first derivative of (2x^3-12x^{4/3}) is 8(x^2-2)(2x^3-12x)^{1/3}

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

8 (x^{2} - 2) (2 x^{3} - 12 x)^{\frac{1}{3}}

Solution steps

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

Apply the chain rule:

\frac{4 ( 2 x ^{3} - 12 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (2 x^{3} - 12 x)

= \frac{4 ( 2 x ^{3} - 12 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (2 x^{3} - 12 x)

\frac{d}{d x} (2 x^{3} - 12 x) = 6 x^{2} - 12

= \frac{4 ( 2 x ^{3} - 12 x ) ^{\frac{1}{3}}}{3} (6 x^{2} - 12)

Simplify

\frac{4 ( 2 x ^{3} - 12 x ) ^{\frac{1}{3}}}{3} (6 x^{2} - 12) : 8 (x^{2} - 2) (2 x^{3} - 12 x)^{\frac{1}{3}}

= 8 (x^{2} - 2) (2 x^{3} - 12 x)^{\frac{1}{3}}

64 y^{^{''}} + 80 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 5

\int 7 arcsin (x) d x

z \to 10 lim (\frac{1}{z - 10})

\int arccos (\frac{1}{x}) d x

\int sin^{2} (y) cos (y) d y

What is the derivative of (2x^3-12x^{4/3}) ?
The derivative of (2x^3-12x^{4/3}) is 8(x^2-2)(2x^3-12x)^{1/3}
What is the first derivative of (2x^3-12x^{4/3}) ?
The first derivative of (2x^3-12x^{4/3}) is 8(x^2-2)(2x^3-12x)^{1/3}