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Popular >

derivative of sqrt(x^3-4x)

Solution

derivative of

x^{3} - 4 x

Solution

\frac{3 x ^{2} - 4}{2 x ^{3} - 4 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2} - 4}{2 x ^{3} - 4 x}

Popular Examples

derivative of 7-x

\frac{d}{d x} (7 - x)

integral of (x^2)/(4x^3+5)

\int \frac{x ^{2}}{4 x ^{3} + 5} d x

derivative of f(x)=5x^3ln(x)derivative of

f (x) = 5 x^{3} ln (x)

y^{''}+2y^'+5y=0,y(0)=5,y^'(0)=-5

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

x^2y^{''}+3xy^'+4y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} + 4 y = 0

Frequently Asked Questions (FAQ)

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