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Popular >

derivative of (x^2+1(x+1)^2)

Solution

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

Solution

4 x^{3} + 6 x^{2} + 4 x + 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x + 1)^{2} + 2 (x + 1) (x^{2} + 1) : 4 x^{3} + 6 x^{2} + 4 x + 2

= 4 x^{3} + 6 x^{2} + 4 x + 2

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+1(x+1)^2) ?
The derivative of (x^2+1(x+1)^2) is 4x^3+6x^2+4x+2
What is the first derivative of (x^2+1(x+1)^2) ?
The first derivative of (x^2+1(x+1)^2) is 4x^3+6x^2+4x+2