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Popular Calculus >

derivative of x^3(x-6)^2

Solution

derivative of

x^{3} (x - 6)^{2}

Solution

5 x^{4} - 48 x^{3} + 108 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (x - 6)^{2})

Apply the Product Rule:

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

f = x^{3}, g = (x - 6)^{2}

= \frac{d}{d x} (x^{3}) (x - 6)^{2} + \frac{d}{d x} ((x - 6)^{2}) x^{3}

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

\frac{d}{d x} ((x - 6)^{2}) = 2 (x - 6)

= 3 x^{2} (x - 6)^{2} + 2 (x - 6) x^{3}

Simplify

3 x^{2} (x - 6)^{2} + 2 (x - 6) x^{3} : 5 x^{4} - 48 x^{3} + 108 x^{2}

= 5 x^{4} - 48 x^{3} + 108 x^{2}

Graph

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

d er i v a t i v e (x - 3)^{- 2}

(dy)/(dx)=(e^x)/(y^2)

\frac{d y}{d x} = \frac{e ^{x}}{y ^{2}}

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\int \frac{x ^{2}}{e ^{x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-6)^2 ?
The derivative of x^3(x-6)^2 is 5x^4-48x^3+108x^2
What is the first derivative of x^3(x-6)^2 ?
The first derivative of x^3(x-6)^2 is 5x^4-48x^3+108x^2