What is the d/(dy)((x)((1+6x)^4)) ?

The d/(dy)((x)((1+6x)^4)) is (1+6y)^4+24y(1+6y)^3

What is the first d/(dy)((x)((1+6x)^4)) ?

The first d/(dy)((x)((1+6x)^4)) is (1+6y)^4+24y(1+6y)^3

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\frac{d}{d y} ((y) ((1 + 6 y)^{4}))

(1 + 6 y)^{4} + 24 y (1 + 6 y)^{3}

Solution steps

\frac{d}{d y} ((y) ((1 + 6 y)^{4}))

Apply the Product Rule:

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

f = y, g = (1 + 6 y)^{4}

= \frac{d y}{d y} (1 + 6 y)^{4} + \frac{d}{d y} ((1 + 6 y)^{4}) y

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

\frac{d}{d y} ((1 + 6 y)^{4}) = 24 (1 + 6 y)^{3}

= 1 \cdot (1 + 6 y)^{4} + 24 (1 + 6 y)^{3} y

Simplify

= (1 + 6 y)^{4} + 24 y (1 + 6 y)^{3}

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What is the d/(dy)((x)((1+6x)^4)) ?
The d/(dy)((x)((1+6x)^4)) is (1+6y)^4+24y(1+6y)^3
What is the first d/(dy)((x)((1+6x)^4)) ?
The first d/(dy)((x)((1+6x)^4)) is (1+6y)^4+24y(1+6y)^3