What is the d/(dy)(e^{x^2+y^2}sin(xy)) ?

The d/(dy)(e^{x^2+y^2}sin(xy)) is e^{x^2+y^2}*2ysin(xy)+cos(xy)xe^{x^2+y^2}

What is the first d/(dy)(e^{x^2+y^2}sin(xy)) ?

The first d/(dy)(e^{x^2+y^2}sin(xy)) is e^{x^2+y^2}*2ysin(xy)+cos(xy)xe^{x^2+y^2}

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Popular >

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

e^{x^{2} + y^{2}} \cdot 2 y sin (x y) + cos (x y) x e^{x^{2} + y^{2}}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = e^{x^{2} + y^{2}}, g = sin (x y)

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

\frac{d}{d y} (e^{x^{2} + y^{2}}) = e^{x^{2} + y^{2}} \cdot 2 y

\frac{d}{d y} (sin (x y)) = cos (x y) x

= e^{x^{2} + y^{2}} \cdot 2 y sin (x y) + cos (x y) x e^{x^{2} + y^{2}}

x^{4} - 3 x

x \to - 0.1 lim (\frac{e ^{x} - 1}{x})

\frac{\partial}{\partial x} (\frac{3}{4 y ^{4} x ^{\frac{1}{4}}})

\frac{d x}{d t} = 7 x t^{4}

\int_{- 1}^{3} (2 x^{2} - 8) d x

What is the d/(dy)(e^{x^2+y^2}sin(xy)) ?
The d/(dy)(e^{x^2+y^2}sin(xy)) is e^{x^2+y^2}*2ysin(xy)+cos(xy)xe^{x^2+y^2}
What is the first d/(dy)(e^{x^2+y^2}sin(xy)) ?
The first d/(dy)(e^{x^2+y^2}sin(xy)) is e^{x^2+y^2}*2ysin(xy)+cos(xy)xe^{x^2+y^2}