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Popular >

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

Solution

derivative of

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

Solution

3 x^{2} - 16 x + 21

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x - 2) = 1

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

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

Simplify

1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 2) : 3 x^{2} - 16 x + 21

= 3 x^{2} - 16 x + 21

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Frequently Asked Questions (FAQ)

What is the derivative of (x-2)(x-3)^2 ?
The derivative of (x-2)(x-3)^2 is 3x^2-16x+21
What is the first derivative of (x-2)(x-3)^2 ?
The first derivative of (x-2)(x-3)^2 is 3x^2-16x+21