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Popular >

derivative of 4/3 x^3+1/2 x-4

Solution

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

Solution

4 x^{2} + \frac{1}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

\frac{d}{d x} (4) = 0

= 4 x^{2} + \frac{1}{2} - 0

Simplify

= 4 x^{2} + \frac{1}{2}

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Frequently Asked Questions (FAQ)

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