What is the derivative of y=(x+1)^2(x^2+2x) ?

The derivative of y=(x+1)^2(x^2+2x) is 4x^3+12x^2+10x+2

What is the first derivative of y=(x+1)^2(x^2+2x) ?

The first derivative of y=(x+1)^2(x^2+2x) is 4x^3+12x^2+10x+2

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derivative of

y = (x + 1)^{2} (x^{2} + 2 x)

4 x^{3} + 12 x^{2} + 10 x + 2

Solution steps

\frac{d}{d x} ((x + 1)^{2} (x^{2} + 2 x))

Apply the Product Rule:

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

f = (x + 1)^{2}, g = x^{2} + 2 x

= \frac{d}{d x} ((x + 1)^{2}) (x^{2} + 2 x) + \frac{d}{d x} (x^{2} + 2 x) (x + 1)^{2}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

\frac{d}{d x} (x^{2} + 2 x) = 2 x + 2

= 2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2}

Simplify

2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2} : 4 x^{3} + 12 x^{2} + 10 x + 2

= 4 x^{3} + 12 x^{2} + 10 x + 2

\frac{tan ( x )}{2}

\frac{x ^{\frac{1}{2}} - 1}{x ^{\frac{1}{2}}}

1 + ln (x)

7 x^{5} + 17

x^{3} - 3 x - 5

What is the derivative of y=(x+1)^2(x^2+2x) ?
The derivative of y=(x+1)^2(x^2+2x) is 4x^3+12x^2+10x+2
What is the first derivative of y=(x+1)^2(x^2+2x) ?
The first derivative of y=(x+1)^2(x^2+2x) is 4x^3+12x^2+10x+2