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Popular >

d/(dy)((x)((1+2x)^6))

Solution

\frac{d}{d y} ((y) ((1 + 2 y)^{6}))

Solution

(1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

Solution steps

\frac{d}{d y} ((y) ((1 + 2 y)^{6}))

Apply the Product Rule:

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

f = y, g = (1 + 2 y)^{6}

= \frac{d y}{d y} (1 + 2 y)^{6} + \frac{d}{d y} ((1 + 2 y)^{6}) y

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

\frac{d}{d y} ((1 + 2 y)^{6}) = 12 (1 + 2 y)^{5}

= 1 \cdot (1 + 2 y)^{6} + 12 (1 + 2 y)^{5} y

Simplify

= (1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

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Frequently Asked Questions (FAQ)

What is the d/(dy)((x)((1+2x)^6)) ?
The d/(dy)((x)((1+2x)^6)) is (1+2y)^6+12y(1+2y)^5
What is the first d/(dy)((x)((1+2x)^6)) ?
The first d/(dy)((x)((1+2x)^6)) is (1+2y)^6+12y(1+2y)^5