What is the derivative of (x-2^2(x+1)) ?

The derivative of (x-2^2(x+1)) is 3x^2-6x

What is the first derivative of (x-2^2(x+1)) ?

The first derivative of (x-2^2(x+1)) is 3x^2-6x

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

3 x^{2} - 6 x

Solution steps

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

Apply the Product Rule:

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

f = (x - 2)^{2}, g = x + 1

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

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

\frac{d}{d x} (x + 1) = 1

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

Simplify

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

= 3 x^{2} - 6 x

\frac{\partial}{\partial y} (x^{2} + y^{2} - 9)

f (x) = 6 x^{2} + x - 3

\frac{t}{2}

y = x, x = 9, y = 0

x y^{^{'}} + 2 y = 8 x^{2}

What is the derivative of (x-2^2(x+1)) ?
The derivative of (x-2^2(x+1)) is 3x^2-6x
What is the first derivative of (x-2^2(x+1)) ?
The first derivative of (x-2^2(x+1)) is 3x^2-6x