What is expand (f(x)+g(x))(f(x)(x)x)' ?

The solution to expand (f(x)+g(x))(f(x)(x)x)' is (x^2f(x)(x))'f(x)+(x^2f(x)(x))'g(x)

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expand (f(x)+g(x))(f(x)(x)x)'

expand

(f (x) + g (x)) (f (x) (x) (x) x)^{'}

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

Solution steps

(f (x) + g (x)) (f (x) (x) (x) x)^{'}

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

Apply the distributive law:

a (b + c) = ab + a c

a = (f (x) (x) (x) x)^{'}, b = f (x), c = g (x)

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

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

Simplify

((x) x f (x) (x))^{'} f (x) + ((x) x f (x) (x))^{'} g (x) : (x^{2} f (x) (x))^{'} f (x) + (x^{2} f (x) (x))^{'} g (x)

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

\frac{10 x ^{\frac{1}{3}} ( x ^{\frac{1}{3}} - 2 )}{3}

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

\frac{b l ( h - 5 )}{2}

\frac{i ( e ^{2 + 3 i} - e ^{- 2 - 3 i} )}{2}

x - y d x + (x + y) d y

What is expand (f(x)+g(x))(f(x)(x)x)' ?
The solution to expand (f(x)+g(x))(f(x)(x)x)' is (x^2f(x)(x))'f(x)+(x^2f(x)(x))'g(x)