What is the derivative of (x^2+1/2 x-4(-x+2)) ?

The derivative of (x^2+1/2 x-4(-x+2)) is -3x^2+3x+5

What is the first derivative of (x^2+1/2 x-4(-x+2)) ?

The first derivative of (x^2+1/2 x-4(-x+2)) is -3x^2+3x+5

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

- 3 x^{2} + 3 x + 5

Solution steps

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

Simplify

(x^{2} + \frac{1}{2} x - 4) (- x + 2) : \frac{- 2 x ^{3} + 3 x ^{2} + 10 x}{2} - 8

= \frac{d}{d x} (\frac{- 2 x ^{3} + 3 x ^{2} + 10 x}{2} - 8)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{- 2 x ^{3} + 3 x ^{2} + 10 x}{2}) - \frac{d}{d x} (8)

\frac{d}{d x} (\frac{- 2 x ^{3} + 3 x ^{2} + 10 x}{2}) = - 3 x^{2} + 3 x + 5

\frac{d}{d x} (8) = 0

= - 3 x^{2} + 3 x + 5 - 0

Simplify

= - 3 x^{2} + 3 x + 5

What is the derivative of (x^2+1/2 x-4(-x+2)) ?
The derivative of (x^2+1/2 x-4(-x+2)) is -3x^2+3x+5
What is the first derivative of (x^2+1/2 x-4(-x+2)) ?
The first derivative of (x^2+1/2 x-4(-x+2)) is -3x^2+3x+5