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Popular >

derivative of x^3(3-x)^4

Solution

derivative of

x^{3} (3 - x)^{4}

Solution

3 x^{2} (3 - x)^{4} - 4 x^{3} (3 - x)^{3}

Solution steps

\frac{d}{d x} (x^{3} (3 - x)^{4})

Apply the Product Rule:

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

f = x^{3}, g = (3 - x)^{4}

= \frac{d}{d x} (x^{3}) (3 - x)^{4} + \frac{d}{d x} ((3 - x)^{4}) x^{3}

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

\frac{d}{d x} ((3 - x)^{4}) = - 4 (3 - x)^{3}

= 3 x^{2} (3 - x)^{4} + (- 4 (3 - x)^{3}) x^{3}

Simplify

= 3 x^{2} (3 - x)^{4} - 4 x^{3} (3 - x)^{3}

Popular Examples

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\frac{d}{d x} (100 + x^{2})

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x(x+y)((dy)/(dx))+y(3x+y)=0

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Frequently Asked Questions (FAQ)

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