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Popular >

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

Solution

derivative of

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

Solution

9 x^{2} - 5 x^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (3 - x^{2}) + (- 2 x) x^{3} : 9 x^{2} - 5 x^{4}

= 9 x^{2} - 5 x^{4}

Popular Examples

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f (x) = \frac{x}{x ^{2} - 7}

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

limit as n approaches 2 of 1/(n^2)

n \to 2 lim (\frac{1}{n ^{2}})

limit as x approaches 2+of sqrt(x^2-4)

x \to 2 + lim (x^{2} - 4)

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

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^3(3-x^2) ?
The derivative of f(x)=x^3(3-x^2) is 9x^2-5x^4
What is the first derivative of f(x)=x^3(3-x^2) ?
The first derivative of f(x)=x^3(3-x^2) is 9x^2-5x^4