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

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

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

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

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derivative of

f (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}

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{12}})

f (x) = 4 x^{5} - x^{3} - 2

x \to + 0 - lim (\frac{e ^{x}}{x ^{3}})

n \to \infty lim (5^{n})

\frac{\partial}{\partial y} (x^{2} - x y + y^{2})

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