What is expand derivative of (x-2(x-5)^3)+12 ?

The solution to expand derivative of (x-2(x-5)^3)+12 is derivative of x^4-17x^3+105x^2-275x+250+12

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expand derivative of (x-2(x-5)^3)+12

expand

\frac{d}{d x} ((x - 2) (x - 5)^{3}) + 12

\frac{d}{d x} (x^{4} - 17 x^{3} + 105 x^{2} - 275 x + 250) + 12

Solution steps

\frac{d}{d x} ((x - 2) (x - 5)^{3}) + 12

\frac{d}{d x} ((x - 2) (x - 5)^{3}) = \frac{d}{d x} (x^{4} - 17 x^{3} + 105 x^{2} - 275 x + 250)

= \frac{d}{d x} (x^{4} - 17 x^{3} + 105 x^{2} - 275 x + 250) + 12

x (1 - \frac{x}{2})

4 (3 + 3)

(x - 1) x

(2 - x 3)^{2}

What is expand derivative of (x-2(x-5)^3)+12 ?
The solution to expand derivative of (x-2(x-5)^3)+12 is derivative of x^4-17x^3+105x^2-275x+250+12