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

The derivative of f(x)=x^2(3-x)^2 is 4x^3-18x^2+18x

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

The first derivative of f(x)=x^2(3-x)^2 is 4x^3-18x^2+18x

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derivative of

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

4 x^{3} - 18 x^{2} + 18 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (3 - x)^{2} + (- 2 (3 - x)) x^{2} : 4 x^{3} - 18 x^{2} + 18 x

= 4 x^{3} - 18 x^{2} + 18 x

x \to - 1 lim (∣ x ∣ - 3)

\int \frac{8}{x ( x + 2 ) ^{3}} d x

\frac{d}{d x} (x ln (2 x))

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

b^{x}

What is the derivative of f(x)=x^2(3-x)^2 ?
The derivative of f(x)=x^2(3-x)^2 is 4x^3-18x^2+18x
What is the first derivative of f(x)=x^2(3-x)^2 ?
The first derivative of f(x)=x^2(3-x)^2 is 4x^3-18x^2+18x