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Popular >

derivative of y=sqrt(3x^3-6x)

Solution

derivative of

y = 3 x^{3} - 6 x

Solution

\frac{9 x ^{2} - 6}{2 3 x ^{3} - 6 x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{3} - 6 x) = 9 x^{2} - 6

= \frac{1}{2 3 x ^{3} - 6 x} (9 x^{2} - 6)

Simplify

\frac{1}{2 3 x ^{3} - 6 x} (9 x^{2} - 6) : \frac{9 x ^{2} - 6}{2 3 x ^{3} - 6 x}

= \frac{9 x ^{2} - 6}{2 3 x ^{3} - 6 x}

Popular Examples

integral of wsqrt(w-3)

\int w w - 3 d w

integral of ((x-5))/(x^2+2x-3)

\int \frac{( x - 5 )}{x ^{2} + 2 x - 3} d x

maclaurin ((e^x+e^{-x}))/2 maclaurin

\frac{( e ^{x} + e ^{- x} )}{2}

derivative of (x-2/3)

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

derivative of-sin^3(x)

\frac{d}{d x} (- sin^{3} (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(3x^3-6x) ?
The derivative of y=sqrt(3x^3-6x) is (9x^2-6)/(2sqrt(3x^3-6x))
What is the first derivative of y=sqrt(3x^3-6x) ?
The first derivative of y=sqrt(3x^3-6x) is (9x^2-6)/(2sqrt(3x^3-6x))