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Popular >

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

Solution

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

Solution

4 x^{3} - 18 x^{2} + 18 x

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}) = 2 x

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

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

Simplify

2 x (x - 3)^{2} + 2 (x - 3) x^{2} : 4 x^{3} - 18 x^{2} + 18 x

= 4 x^{3} - 18 x^{2} + 18 x

Popular Examples

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f (x) = 8 x, (16, 32)

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y = ln (3 x^{2} cot (sec^{2} (4 x)))

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- 8 x^{2} - 2 x

limit as t approaches 1 of (e^t-e)/(t-1)

t \to 1 lim (\frac{e ^{t} - e}{t - 1})

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\frac{d}{d x} (x^{2} - 16 I n (x^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of x^2(x-3^2) ?
The derivative of x^2(x-3^2) is 4x^3-18x^2+18x
What is the first derivative of x^2(x-3^2) ?
The first derivative of x^2(x-3^2) is 4x^3-18x^2+18x