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Popular >

derivative of \sqrt[3]{(2-3x^2})

Solution

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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

integral of (12)/(x^2-9)

\int \frac{12}{x ^{2} - 9} d x

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\frac{d}{d x} (\frac{1 + csc ( x ^{5} )}{1 - cot ( x ^{5} )})

integral of (y^3)/3

\int \frac{y ^{3}}{3} d y

(\partial)/(\partial x)(2yarctan(x/y))

\frac{\partial}{\partial x} (2 y arctan (\frac{x}{y}))

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{(2-3x^2}) ?
The derivative of \sqrt[3]{(2-3x^2}) is -2/((2-3x)^{1/3)}
What is the first derivative of \sqrt[3]{(2-3x^2}) ?
The first derivative of \sqrt[3]{(2-3x^2}) is -2/((2-3x)^{1/3)}