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

The derivative of y=x(x-6)^2 is 3x^2-24x+36

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

The first derivative of y=x(x-6)^2 is 3x^2-24x+36

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derivative of

y = x (x - 6)^{2}

3 x^{2} - 24 x + 36

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 6)^{2}

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

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

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

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

Simplify

1 \cdot (x - 6)^{2} + 2 (x - 6) x : 3 x^{2} - 24 x + 36

= 3 x^{2} - 24 x + 36

e^{- 5 x} + e^{3 x}

\frac{d}{d x} (e^{x} + 19)

x \to 2 + lim (2 - x)

\frac{d}{d x} (\frac{1 - 6 x}{2 + x})

(t^{2} + e^{t}) t

What is the derivative of y=x(x-6)^2 ?
The derivative of y=x(x-6)^2 is 3x^2-24x+36
What is the first derivative of y=x(x-6)^2 ?
The first derivative of y=x(x-6)^2 is 3x^2-24x+36