What is the derivative of f(x)=6x^2(x-9) ?

The derivative of f(x)=6x^2(x-9) is 6(3x^2-18x)

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

The first derivative of f(x)=6x^2(x-9) is 6(3x^2-18x)

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derivative of

f (x) = 6 x^{2} (x - 9)

6 (3 x^{2} - 18 x)

Solution steps

\frac{d}{d x} (6 x^{2} (x - 9))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = x - 9

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

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

\frac{d}{d x} (x - 9) = 1

= 6 (2 x (x - 9) + 1 \cdot x^{2})

Simplify

6 (2 x (x - 9) + 1 \cdot x^{2}) : 6 (3 x^{2} - 18 x)

= 6 (3 x^{2} - 18 x)

\frac{\partial}{\partial x} (\frac{2}{x ^{3}})

\int \frac{4 x ^{2} - 9}{x} d x

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

\int e^{x} + 9 x d x

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

What is the derivative of f(x)=6x^2(x-9) ?
The derivative of f(x)=6x^2(x-9) is 6(3x^2-18x)
What is the first derivative of f(x)=6x^2(x-9) ?
The first derivative of f(x)=6x^2(x-9) is 6(3x^2-18x)