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Popular >

derivative of (x+1)^2(x-4)^3

Solution

derivative of

(x + 1)^{2} (x - 4)^{3}

Solution

2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}

Solution steps

\frac{d}{d x} ((x + 1)^{2} (x - 4)^{3})

Apply the Product Rule:

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

f = (x + 1)^{2}, g = (x - 4)^{3}

= \frac{d}{d x} ((x + 1)^{2}) (x - 4)^{3} + \frac{d}{d x} ((x - 4)^{3}) (x + 1)^{2}

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

\frac{d}{d x} ((x - 4)^{3}) = 3 (x - 4)^{2}

= 2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}

Popular Examples

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(- 2, 3), (4, - 1)

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(- 1, - 1), (1, 2)

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f (x) = cos (8 0^{\circ})

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f (x) = x^{2} + 18 x + 86

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Frequently Asked Questions (FAQ)

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