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

The derivative of (x-4(x/2+1)^3) is (2x^3+3x^2-12x-20)/4

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

The first derivative of (x-4(x/2+1)^3) is (2x^3+3x^2-12x-20)/4

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

\frac{2 x ^{3} + 3 x ^{2} - 12 x - 20}{4}

Solution steps

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

Simplify

(x - 4) (\frac{x}{2} + 1)^{3} : \frac{x ^{4} + 2 x ^{3} - 12 x ^{2} - 40 x}{8} - 4

= \frac{d}{d x} (\frac{x ^{4} + 2 x ^{3} - 12 x ^{2} - 40 x}{8} - 4)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4} + 2 x ^{3} - 12 x ^{2} - 40 x}{8}) - \frac{d}{d x} (4)

\frac{d}{d x} (\frac{x ^{4} + 2 x ^{3} - 12 x ^{2} - 40 x}{8}) = \frac{2 x ^{3} + 3 x ^{2} - 12 x - 20}{4}

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

= \frac{2 x ^{3} + 3 x ^{2} - 12 x - 20}{4} - 0

Simplify

= \frac{2 x ^{3} + 3 x ^{2} - 12 x - 20}{4}

\frac{\partial}{\partial x} (7 e^{x y + 8})

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

\int e^{7 x - 5} d x

3 u

f (x) = 2 x^{2} - 3 x + 1, (2, 3)

What is the derivative of (x-4(x/2+1)^3) ?
The derivative of (x-4(x/2+1)^3) is (2x^3+3x^2-12x-20)/4
What is the first derivative of (x-4(x/2+1)^3) ?
The first derivative of (x-4(x/2+1)^3) is (2x^3+3x^2-12x-20)/4