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

The derivative of (x+6(x-2)^2) is 3x^2+4x-20

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

The first derivative of (x+6(x-2)^2) is 3x^2+4x-20

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

3 x^{2} + 4 x - 20

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x + 6) = 1

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

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

Simplify

1 \cdot (x - 2)^{2} + 2 (x - 2) (x + 6) : 3 x^{2} + 4 x - 20

= 3 x^{2} + 4 x - 20

What is the derivative of (x+6(x-2)^2) ?
The derivative of (x+6(x-2)^2) is 3x^2+4x-20
What is the first derivative of (x+6(x-2)^2) ?
The first derivative of (x+6(x-2)^2) is 3x^2+4x-20