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Popular >

derivative of (x+2)^2*(x-3)^3

Solution

derivative of

(x + 2)^{2} \cdot (x - 3)^{3}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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