What is the derivative of (2x^3+x^2-6x^{2/3}) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

x \to 2 lim (\frac{x}{x ^{2} - x - 2})

\int_{0}^{6} 2 x^{2} - 16 x + 30 d x

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

f (x) = 13 x^{- 3}

x \to 0 lim ((1 + 3 x)^{\frac{5}{x}})

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