What is expand (x+5)^3y'(x) ?

The solution to expand (x+5)^3y'(x) is x^3y'(x)+15x^2y'(x)+75xy'(x)+125y'(x)

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expand (x+5)^3y'(x)

expand

(x + 5)^{3} y^{'} (x)

x^{3} y' (x) + 15 x^{2} y' (x) + 75 x y' (x) + 125 y' (x)

Solution steps

(x + 5)^{3} y^{'} (x)

(x + 5)^{3} = x^{3} + 15 x^{2} + 75 x + 125

= (x^{3} + 15 x^{2} + 75 x + 125) y^{^{'}} (x)

Distribute parentheses

= y^{^{'}} (x) x^{3} + y^{^{'}} (x) 15 x^{2} + y^{^{'}} (x) 75 x + y^{^{'}} (x) 125

= x^{3} y^{^{'}} (x) + 15 x^{2} y^{^{'}} (x) + 75 x y^{^{'}} (x) + 125 y^{^{'}} (x)

(4 t^{3}) (t^{2 + 5})

(2 + 3 x - 4 x^{2})^{5}

\frac{9 ( x + h ) - 9 x ^{2}}{h}

(6 x^{3} + 7) \cdot (e^{x})

m (m - 7 = 0)

What is expand (x+5)^3y'(x) ?
The solution to expand (x+5)^3y'(x) is x^3y'(x)+15x^2y'(x)+75xy'(x)+125y'(x)