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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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