What is (\partial)/(\partial y)(sin(xy^2+y)+2e^x) ?

The answer to (\partial)/(\partial y)(sin(xy^2+y)+2e^x) is cos(xy^2+y)(2xy+1)

Popular >

(\partial)/(\partial y)(sin(xy^2+y)+2e^x)

\frac{\partial}{\partial y} (sin (x y^{2} + y) + 2 e^{x})

cos (x y^{2} + y) (2 x y + 1)

Solution steps

\frac{\partial}{\partial y} (sin (x y^{2} + y) + 2 e^{x})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (sin (x y^{2} + y)) + \frac{\partial}{\partial y} (2 e^{x})

\frac{\partial}{\partial y} (sin (x y^{2} + y)) = cos (x y^{2} + y) (2 x y + 1)

\frac{\partial}{\partial y} (2 e^{x}) = 0

= cos (x y^{2} + y) (2 x y + 1) + 0

Simplify

= cos (x y^{2} + y) (2 x y + 1)

n = 1 \sum \infty \frac{1 + 5 ^{n}}{7 ^{n}}

\frac{d}{d x} (e^{3 x} y)

\int x^{- 3.5} d x

n = 1.0 E 22 \sum \infty \frac{1}{n ^{2}}

f (x) = x e^{- x}, at x = 2

What is (\partial)/(\partial y)(sin(xy^2+y)+2e^x) ?
The answer to (\partial)/(\partial y)(sin(xy^2+y)+2e^x) is cos(xy^2+y)(2xy+1)