What is the first d/(dy)((x)(4x-3)) ?

The first d/(dy)((x)(4x-3)) is 8y-3

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d/(dy)((x)(4x-3))

\frac{d}{d y} ((y) (4 y - 3))

8 y - 3

Solution steps

\frac{d}{d y} ((y) (4 y - 3))

Apply the Product Rule:

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

f = y, g = 4 y - 3

= \frac{d y}{d y} (4 y - 3) + \frac{d}{d y} (4 y - 3) y

\frac{d y}{d y} = 1

\frac{d}{d y} (4 y - 3) = 4

= 1 \cdot (4 y - 3) + 4 y

Simplify

= 8 y - 3

- (b)

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