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Popular >

derivative of (x^4/2-3/2 x^2-x)

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d x}{d x} = 1

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

Popular Examples

limit as x approaches-2 of x^2-5

x \to - 2 lim (x^{2} - 5)

integral from 1 to infinity of x^{-4/5}

\int_{1}^{\infty} x^{- \frac{4}{5}} d x

f^{^{'}} (x) = 6 x

derivative of f(x)= 2/(3x)derivative of

f (x) = \frac{2}{3 x}

derivative of (3x^2/(x^2-4))

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

Frequently Asked Questions (FAQ)

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