What is the derivative of 1/3 x^3-7/2 x^2-8x+3 ?

The derivative of 1/3 x^3-7/2 x^2-8x+3 is x^2-7x-8

What is the first derivative of 1/3 x^3-7/2 x^2-8x+3 ?

The first derivative of 1/3 x^3-7/2 x^2-8x+3 is x^2-7x-8

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derivative of

\frac{1}{3} x^{3} - \frac{7}{2} x^{2} - 8 x + 3

x^{2} - 7 x - 8

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{3} - \frac{7}{2} x^{2} - 8 x + 3)

Simplify

\frac{1}{3} x^{3} - \frac{7}{2} x^{2} - 8 x + 3 : \frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} - 8 x + 3

= \frac{d}{d x} (\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} - 8 x + 3)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (\frac{7 x ^{2}}{2}) - \frac{d}{d x} (8 x) + \frac{d}{d x} (3)

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

\frac{d}{d x} (\frac{7 x ^{2}}{2}) = 7 x

\frac{d}{d x} (8 x) = 8

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

= x^{2} - 7 x - 8 + 0

Simplify

= x^{2} - 7 x - 8

What is the derivative of 1/3 x^3-7/2 x^2-8x+3 ?
The derivative of 1/3 x^3-7/2 x^2-8x+3 is x^2-7x-8
What is the first derivative of 1/3 x^3-7/2 x^2-8x+3 ?
The first derivative of 1/3 x^3-7/2 x^2-8x+3 is x^2-7x-8