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

The derivative of (x-4^3+3x(x-4)^2) is 12x^2-72x+96

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

The first derivative of (x-4^3+3x(x-4)^2) is 12x^2-72x+96

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

12 x^{2} - 72 x + 96

Solution steps

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

Simplify

(x - 4)^{3} + 3 x (x - 4)^{2} : 4 x^{3} - 36 x^{2} + 96 x - 64

= \frac{d}{d x} (4 x^{3} - 36 x^{2} + 96 x - 64)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (96 x) - \frac{d}{d x} (64)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (96 x) = 96

\frac{d}{d x} (64) = 0

= 12 x^{2} - 72 x + 96 - 0

Simplify

= 12 x^{2} - 72 x + 96

\int (2 sin (4 x) - 8 cos (3 x)) d x

\int_{0}^{1} x e^{- 5 x} d x

\frac{d}{d x} ((x + 4)^{3} (x - 3)^{6})

x \to 4 lim (2 - x)

y = 3 x - 7 x

What is the derivative of (x-4^3+3x(x-4)^2) ?
The derivative of (x-4^3+3x(x-4)^2) is 12x^2-72x+96
What is the first derivative of (x-4^3+3x(x-4)^2) ?
The first derivative of (x-4^3+3x(x-4)^2) is 12x^2-72x+96