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Popular >

derivative of 1/3 x^3+1/2 x^2+2

Solution

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

Solution

x^{2} + x

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (2) = 0

= x^{2} + x + 0

Simplify

= x^{2} + x

Popular Examples

y^{''}-2/x y^'-(10)/(x^2)=0

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{10}{x ^{2}} = 0

integral of 2x(x^2+5)^7

\int 2 x (x^{2} + 5)^{7} d x

(\partial)/(\partial x)(cos(x^2+y^3))

\frac{\partial}{\partial x} (cos (x^{2} + y^{3}))

limit as x approaches pi of 1/(cos(x))

x \to π lim (\frac{1}{cos ( x )})

derivative of f(x)= x/(x^2+11)derivative of

f (x) = \frac{x}{x ^{2} + 11}

Frequently Asked Questions (FAQ)

What is the derivative of 1/3 x^3+1/2 x^2+2 ?
The derivative of 1/3 x^3+1/2 x^2+2 is x^2+x
What is the first derivative of 1/3 x^3+1/2 x^2+2 ?
The first derivative of 1/3 x^3+1/2 x^2+2 is x^2+x