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Popular >

derivative of (x+1^2(x+2)^3)

Solution

\frac{d}{d x} ((x + 1)^{2} (x + 2)^{3})

Solution

2 (x + 1) (x + 2)^{3} + 3 (x + 2)^{2} (x + 1)^{2}

Solution steps

\frac{d}{d x} ((x + 1)^{2} (x + 2)^{3})

Apply the Product Rule:

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

f = (x + 1)^{2}, g = (x + 2)^{3}

= \frac{d}{d x} ((x + 1)^{2}) (x + 2)^{3} + \frac{d}{d x} ((x + 2)^{3}) (x + 1)^{2}

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

\frac{d}{d x} ((x + 2)^{3}) = 3 (x + 2)^{2}

= 2 (x + 1) (x + 2)^{3} + 3 (x + 2)^{2} (x + 1)^{2}

Popular Examples

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tangent of f(x)=x^2-sqrt(x),(1,0)tangent of

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Frequently Asked Questions (FAQ)

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