What is (\partial)/(\partial y)(y(x+y+1)) ?

The answer to (\partial)/(\partial y)(y(x+y+1)) is 2y+x+1

Popular >

(\partial)/(\partial y)(y(x+y+1))

\frac{\partial}{\partial y} (y (x + y + 1))

2 y + x + 1

Solution steps

\frac{\partial}{\partial y} (y (x + y + 1))

Treat

x

as a constant

Apply the Product Rule:

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

f = y, g = x + y + 1

= \frac{\partial}{\partial y} (y) (x + y + 1) + \frac{\partial}{\partial y} (x + y + 1) y

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (x + y + 1) = 1

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

Simplify

1 \cdot (x + y + 1) + 1 \cdot y : 2 y + x + 1

= 2 y + x + 1

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

\int \frac{1}{( x ^{2} - 2 x + 2 ) ^{2}} d x

\int \frac{4}{1 - x ^{2}} d x

\frac{d}{d x} (\frac{4 x ^{3} - 2 x + 1}{x ^{2}})

\int_{0}^{2 π} 3 sin (2 x) d x

What is (\partial)/(\partial y)(y(x+y+1)) ?
The answer to (\partial)/(\partial y)(y(x+y+1)) is 2y+x+1