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

The derivative of f(x)=x^3(x-9)^2 is 5x^4-72x^3+243x^2

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

The first derivative of f(x)=x^3(x-9)^2 is 5x^4-72x^3+243x^2

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derivative of

f (x) = x^{3} (x - 9)^{2}

5 x^{4} - 72 x^{3} + 243 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (x - 9)^{2})

Apply the Product Rule:

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

f = x^{3}, g = (x - 9)^{2}

= \frac{d}{d x} (x^{3}) (x - 9)^{2} + \frac{d}{d x} ((x - 9)^{2}) x^{3}

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

\frac{d}{d x} ((x - 9)^{2}) = 2 (x - 9)

= 3 x^{2} (x - 9)^{2} + 2 (x - 9) x^{3}

Simplify

3 x^{2} (x - 9)^{2} + 2 (x - 9) x^{3} : 5 x^{4} - 72 x^{3} + 243 x^{2}

= 5 x^{4} - 72 x^{3} + 243 x^{2}

What is the derivative of f(x)=x^3(x-9)^2 ?
The derivative of f(x)=x^3(x-9)^2 is 5x^4-72x^3+243x^2
What is the first derivative of f(x)=x^3(x-9)^2 ?
The first derivative of f(x)=x^3(x-9)^2 is 5x^4-72x^3+243x^2