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

The derivative of x(3x-9^3) is (3x-9)^3+9x(3x-9)^2

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

The first derivative of x(3x-9^3) is (3x-9)^3+9x(3x-9)^2

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot (3 x - 9)^{3} + 9 (3 x - 9)^{2} x

Simplify

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

\int_{0}^{5} \frac{2 x - 1}{x + 1} d x

\int_{0}^{2} x e^{- x^{2}} d x

\int ∣ x ∣ d x

\frac{\partial}{\partial x} (a^{x} - b^{x})

\int t^{2} e^{- 22 t} d t

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