What is the first d/(dy)((x)(2x+1)) ?

The first d/(dy)((x)(2x+1)) is 4y+1

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

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

4 y + 1

Solution steps

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

Apply the Product Rule:

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

f = y, g = 2 y + 1

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

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

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

= 1 \cdot (2 y + 1) + 2 y

Simplify

= 4 y + 1

\frac{sec ^{2} ( x ) ( x ^{2} + 1 ) ^{6}}{( e ^{x} - cos ^{2} ( x ) ) ^{4}}

1 + t^{2} \cdot (1 + t^{2})

(2 x - y) (2 x + y)

d x (- \frac{7}{3 x ^{3}} + x + \frac{5}{x})

x (π - x)