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

The derivative of f(x)=x^2(2x+9)^3 is 2x(2x+9)^3+6(2x+9)^2x^2

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

The first derivative of f(x)=x^2(2x+9)^3 is 2x(2x+9)^3+6(2x+9)^2x^2

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derivative of

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

2 x (2 x + 9)^{3} + 6 (2 x + 9)^{2} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((2 x + 9)^{3}) = 6 (2 x + 9)^{2}

= 2 x (2 x + 9)^{3} + 6 (2 x + 9)^{2} x^{2}

What is the derivative of f(x)=x^2(2x+9)^3 ?
The derivative of f(x)=x^2(2x+9)^3 is 2x(2x+9)^3+6(2x+9)^2x^2
What is the first derivative of f(x)=x^2(2x+9)^3 ?
The first derivative of f(x)=x^2(2x+9)^3 is 2x(2x+9)^3+6(2x+9)^2x^2