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Popular >

(\partial)/(\partial y)(ye^{xy}+sin(y))

Solution

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

Solution

e^{x y} + x e^{x y} y + cos (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (sin (y)) = cos (y)

= e^{x y} + x e^{x y} y + cos (y)

Popular Examples

integral of e^{ax}sin(bx)

\int e^{a x} sin (b x) d x

(\partial)/(\partial x)(e^{-x}sin(y)z)

\frac{\partial}{\partial x} (e^{- x} sin (y) z)

sum from n=1 to infinity of (3n)/(6n+13)

n = 1 \sum \infty \frac{3 n}{6 n + 13}

integral of 1/(xln^2(x))

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

f (x) = cos (4 x + 1)

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial y)(ye^{xy}+sin(y)) ?
The answer to (\partial)/(\partial y)(ye^{xy}+sin(y)) is e^{xy}+xe^{xy}y+cos(y)