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Popular >

derivative of y=(x^2-4)(2x-6)

Solution

derivative of

y = (x^{2} - 4) (2 x - 6)

Solution

6 x^{2} - 12 x - 8

Solution steps

\frac{d}{d x} ((x^{2} - 4) (2 x - 6))

Apply the Product Rule:

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

f = x^{2} - 4, g = 2 x - 6

= \frac{d}{d x} (x^{2} - 4) (2 x - 6) + \frac{d}{d x} (2 x - 6) (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = 2 x

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

= 2 x (2 x - 6) + 2 (x^{2} - 4)

Simplify

2 x (2 x - 6) + 2 (x^{2} - 4) : 6 x^{2} - 12 x - 8

= 6 x^{2} - 12 x - 8

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Frequently Asked Questions (FAQ)

What is the derivative of y=(x^2-4)(2x-6) ?
The derivative of y=(x^2-4)(2x-6) is 6x^2-12x-8
What is the first derivative of y=(x^2-4)(2x-6) ?
The first derivative of y=(x^2-4)(2x-6) is 6x^2-12x-8