What is expand f'(x)(x+4)^2(x-3) ?

The solution to expand f'(x)(x+4)^2(x-3) is x^3f'(x)+5x^2f'(x)-8xf'(x)-48f'(x)

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expand f'(x)(x+4)^2(x-3)

expand

f^{'} (x) (x + 4)^{2} (x - 3)

x^{3} f' (x) + 5 x^{2} f' (x) - 8 x f' (x) - 48 f' (x)

Solution steps

f^{'} (x) (x + 4)^{2} (x - 3)

Apply the distributive law:

a (b - c) = ab - a c

a = f^{'} (x) (x + 4)^{2}, b = x, c = 3

= f^{^{'}} (x) (x + 4)^{2} x - f^{^{'}} (x) (x + 4)^{2} \cdot 3

= x f^{^{'}} (x) (x + 4)^{2} - 3 f^{^{'}} (x) (x + 4)^{2}

Simplify

x f^{'} (x) (x + 4)^{2} - 3 f^{'} (x) (x + 4)^{2} : x^{3} f^{'} (x) + 5 x^{2} f^{'} (x) - 8 x f^{'} (x) - 48 f^{'} (x)

= x^{3} f^{'} (x) + 5 x^{2} f^{'} (x) - 8 x f^{'} (x) - 48 f^{'} (x)

5 (2 + 1)

\frac{( a + b ) x + ( a - b ) ∣ x ∣}{2 x}

\frac{1}{2} (- \frac{1}{4} cos (4 θ) - \frac{1}{2} cos (2 θ))

(- 1, cos (t)) \cdot (2 sin (t), 3 π - 3 t)

What is expand f'(x)(x+4)^2(x-3) ?
The solution to expand f'(x)(x+4)^2(x-3) is x^3f'(x)+5x^2f'(x)-8xf'(x)-48f'(x)