What is the derivative of 2/3 x^3+x^2-12x+17 ?

The derivative of 2/3 x^3+x^2-12x+17 is 2x^2+2x-12

What is the first derivative of 2/3 x^3+x^2-12x+17 ?

The first derivative of 2/3 x^3+x^2-12x+17 is 2x^2+2x-12

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\frac{d}{d x} (\frac{2}{3} x^{3} + x^{2} - 12 x + 17)

2 x^{2} + 2 x - 12

Solution steps

\frac{d}{d x} (\frac{2}{3} x^{3} + x^{2} - 12 x + 17)

Simplify

\frac{2}{3} x^{3} + x^{2} - 12 x + 17 : \frac{2 x ^{3}}{3} + x^{2} - 12 x + 17

= \frac{d}{d x} (\frac{2 x ^{3}}{3} + x^{2} - 12 x + 17)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{2 x ^{3}}{3}) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (12 x) + \frac{d}{d x} (17)

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

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

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (17) = 0

= 2 x^{2} + 2 x - 12 + 0

Simplify

= 2 x^{2} + 2 x - 12

\frac{x ^{2} - 2 x - 8}{x + 2}

y^{^{''}} + 12 y^{^{'}} + 36 y = e^{- 7 x} (x^{2} + 3 x + 6)

f (x) = \frac{1}{( x ^{3} + 8 ) ^{5}}

\frac{d}{d x} (I n 3 x + 4)

\frac{s - 8}{2 s ^{2} + s + 12}

What is the derivative of 2/3 x^3+x^2-12x+17 ?
The derivative of 2/3 x^3+x^2-12x+17 is 2x^2+2x-12
What is the first derivative of 2/3 x^3+x^2-12x+17 ?
The first derivative of 2/3 x^3+x^2-12x+17 is 2x^2+2x-12