What is the derivative of x(4x-12^3) ?

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

What is the first derivative of x(4x-12^3) ?

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

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

(4 x - 12)^{3} + 12 x (4 x - 12)^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (4 x - 12)^{3}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (4 x - 12)^{3} + 12 (4 x - 12)^{2} x

Simplify

= (4 x - 12)^{3} + 12 x (4 x - 12)^{2}

\int - \frac{4000}{x ^{2}} d x

\frac{d}{d x} (sin^{2} (x) cos^{3} (x))

x \to 0 lim (x sin (\frac{4}{x}))

y^{^{'}} + y + 2 cos (x) = 0

\int_{4}^{6} \frac{1}{x} d x

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