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Popular >

derivative of y=(3x^2+2)(2x-7)

Solution

derivative of

y = (3 x^{2} + 2) (2 x - 7)

Solution

18 x^{2} - 42 x + 4

Solution steps

\frac{d}{d x} ((3 x^{2} + 2) (2 x - 7))

Apply the Product Rule:

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

f = 3 x^{2} + 2, g = 2 x - 7

= \frac{d}{d x} (3 x^{2} + 2) (2 x - 7) + \frac{d}{d x} (2 x - 7) (3 x^{2} + 2)

\frac{d}{d x} (3 x^{2} + 2) = 6 x

\frac{d}{d x} (2 x - 7) = 2

= 6 x (2 x - 7) + 2 (3 x^{2} + 2)

Simplify

6 x (2 x - 7) + 2 (3 x^{2} + 2) : 18 x^{2} - 42 x + 4

= 18 x^{2} - 42 x + 4

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Frequently Asked Questions (FAQ)

What is the derivative of y=(3x^2+2)(2x-7) ?
The derivative of y=(3x^2+2)(2x-7) is 18x^2-42x+4
What is the first derivative of y=(3x^2+2)(2x-7) ?
The first derivative of y=(3x^2+2)(2x-7) is 18x^2-42x+4