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Popular >

derivative of ({f}(x)(4x^3-4x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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