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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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