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Popular >

derivative of f(x)= 1/2 x^3-2x+3

Solution

derivative of

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

Solution

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

Solution steps

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

Simplify

\frac{1}{2} x^{3} - 2 x + 3 : \frac{x ^{3}}{2} - 2 x + 3

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (3) = 0

= \frac{3 x ^{2}}{2} - 2 + 0

Simplify

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

Popular Examples

integral of (12x^3-24x^2+7)/(x^2-2x)

\int \frac{12 x ^{3} - 24 x ^{2} + 7}{x ^{2} - 2 x} d x

derivative of (sqrt(s)-3)/(sqrt(s)+7)derivative of

\frac{s - 3}{s + 7}

limit as x approaches-2 of (-1)/(-x^2+4)

x \to - 2 lim (\frac{- 1}{- x ^{2} + 4})

(dy)/(dx)=4x+(9x^2)/((3x^3+1)^{3/2)}

\frac{d y}{d x} = 4 x + \frac{9 x ^{2}}{( 3 x ^{3} + 1 ) ^{\frac{3}{2}}}

integral from 0 to 1 of (3x+1)cos(x)

\int_{0}^{1} (3 x + 1) cos (x) d x

Frequently Asked Questions (FAQ)

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