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Popular >

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

Solution

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

Solution

5 x^{4} - 24 x^{3} + 27 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (x - 3)^{2} + 2 (x - 3) x^{3} : 5 x^{4} - 24 x^{3} + 27 x^{2}

= 5 x^{4} - 24 x^{3} + 27 x^{2}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-3^2) ?
The derivative of x^3(x-3^2) is 5x^4-24x^3+27x^2
What is the first derivative of x^3(x-3^2) ?
The first derivative of x^3(x-3^2) is 5x^4-24x^3+27x^2