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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{2} (3 x^{2} + 0)

Simplify

\frac{1}{2} (3 x^{2} + 0) : \frac{3 x ^{2}}{2}

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

Popular Examples

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

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

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\frac{\partial}{\partial x} (x^{2} + (y - 1)^{2})

integral from-4 to 4 of 1/(sqrt(16-x^2))

\int_{- 4}^{4} \frac{1}{16 - x ^{2}} d x

(\partial)/(\partial x)(sqrt(2x+1)+ye^{-x})

\frac{\partial}{\partial x} (2 x + 1 + y e^{- x})

integral of cos(x)(8+7sin^2(x))

\int cos (x) (8 + 7 sin^{2} (x)) d x

Frequently Asked Questions (FAQ)

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