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

The derivative of x(x-9^2) is 3x^2-36x+81

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

The first derivative of x(x-9^2) is 3x^2-36x+81

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

3 x^{2} - 36 x + 81

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x - 9)^{2} + 2 (x - 9) x : 3 x^{2} - 36 x + 81

= 3 x^{2} - 36 x + 81

\frac{x d y}{d x} = y + x^{2} sin (x)

\int (\frac{1}{3} x - 9)^{\frac{2}{3}} d x

\int - 25 sin (5 x) d x

\frac{d y}{d t} = 45 t^{8}

\frac{d}{d x} (3 (ln (x) + 1))

What is the derivative of x(x-9^2) ?
The derivative of x(x-9^2) is 3x^2-36x+81
What is the first derivative of x(x-9^2) ?
The first derivative of x(x-9^2) is 3x^2-36x+81