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Popular >

derivative of f(x)=(x-1)^2(x-2)^3

Solution

derivative of

f (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}

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Frequently Asked Questions (FAQ)

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