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Popular Calculus >

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

Solution

derivative of

x (x - 3)^{2}

Solution

\frac{5 x ^{2} - 18 x + 9}{2 x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

\frac{1}{2 x} (x - 3)^{2} + 2 (x - 3) x : \frac{5 x ^{2} - 18 x + 9}{2 x}

= \frac{5 x ^{2} - 18 x + 9}{2 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x-3)^2 ?
The derivative of sqrt(x)(x-3)^2 is (5x^2-18x+9)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-3)^2 ?
The first derivative of sqrt(x)(x-3)^2 is (5x^2-18x+9)/(2sqrt(x))