What is the derivative of f(x(2x^2-4)) ?

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

What is the first derivative of f(x(2x^2-4)) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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