What is the derivative of ({f}(x)(12x^2-4x+1)) ?

The derivative of ({f}(x)(12x^2-4x+1)) is derivative of {f}(x)(12x^2-4x+1)+(24x-4){f}(x)

What is the first derivative of ({f}(x)(12x^2-4x+1)) ?

The first derivative of ({f}(x)(12x^2-4x+1)) is derivative of {f}(x)(12x^2-4x+1)+(24x-4){f}(x)

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\frac{d}{d x} ((f (x)) (12 x^{2} - 4 x + 1))

\frac{d}{d x} (f (x)) (12 x^{2} - 4 x + 1) + (24 x - 4) f (x)

Solution steps

\frac{d}{d x} ((f (x)) (12 x^{2} - 4 x + 1))

Apply the Product Rule:

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

f = f (x), g = 12 x^{2} - 4 x + 1

= \frac{d}{d x} (f (x)) (12 x^{2} - 4 x + 1) + \frac{d}{d x} (12 x^{2} - 4 x + 1) f (x)

\frac{d}{d x} (12 x^{2} - 4 x + 1) = 24 x - 4

= \frac{d}{d x} (f (x)) (12 x^{2} - 4 x + 1) + (24 x - 4) f (x)

\frac{x - 3}{5 x}

e^{2 x} (1 + 2 x)

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

\frac{1}{( 4 s ^{2} + 4 s + 5 ) ^{2}}

\frac{x ( x + 3 )}{( x + 2 ) ^{2} ( 7 x - 3 )}

What is the derivative of ({f}(x)(12x^2-4x+1)) ?
The derivative of ({f}(x)(12x^2-4x+1)) is derivative of {f}(x)(12x^2-4x+1)+(24x-4){f}(x)
What is the first derivative of ({f}(x)(12x^2-4x+1)) ?
The first derivative of ({f}(x)(12x^2-4x+1)) is derivative of {f}(x)(12x^2-4x+1)+(24x-4){f}(x)