What is the (f(x)(2x))' ?

The (f(x)(2x))' is 2(xf'(x)+f(x))

What is the first (f(x)(2x))' ?

The first (f(x)(2x))' is 2(xf'(x)+f(x))

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(f (x) (2 x))^{'}

2 (x f' (x) + f (x))

Solution steps

(f (x) (2 x))^{'}

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 (f (x) x)^{^{'}}

Apply the Product Rule:

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

f = f (x), g = x

= 2 (f^{^{'}} (x) x + x^{^{'}} f (x))

x^{'} = 1

= 2 (f^{^{'}} (x) x + 1 \cdot f (x))

Simplify

= 2 (x f^{^{'}} (x) + f (x))

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