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

The d/(dy)(e^{x^2-y^2}cos(2xy)) is -2e^{x^2-y^2}ycos(2xy)-2e^{x^2-y^2}xsin(2xy)

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

The first d/(dy)(e^{x^2-y^2}cos(2xy)) is -2e^{x^2-y^2}ycos(2xy)-2e^{x^2-y^2}xsin(2xy)

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\frac{d}{d y} (e^{x^{2} - y^{2}} cos (2 x y))

- 2 e^{x^{2} - y^{2}} y cos (2 x y) - 2 e^{x^{2} - y^{2}} x sin (2 x y)

Solution steps

\frac{d}{d y} (e^{x^{2} - y^{2}} cos (2 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 = cos (2 x y)

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

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

\frac{d}{d y} (cos (2 x y)) = - sin (2 x y) \cdot 2 x

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

Simplify

= - 2 e^{x^{2} - y^{2}} y cos (2 x y) - 2 e^{x^{2} - y^{2}} x sin (2 x y)

x \to 0 lim (\frac{5 x ^{2} - 2 x}{x})

\int \frac{250}{( x ^{2} + 25 ) ^{2}} d x

y = e^{s i n (x)}

\frac{s - 9}{2 s ^{2} + s + 4}

k = 0 \sum \infty (- 1)^{k}

What is the d/(dy)(e^{x^2-y^2}cos(2xy)) ?
The d/(dy)(e^{x^2-y^2}cos(2xy)) is -2e^{x^2-y^2}ycos(2xy)-2e^{x^2-y^2}xsin(2xy)
What is the first d/(dy)(e^{x^2-y^2}cos(2xy)) ?
The first d/(dy)(e^{x^2-y^2}cos(2xy)) is -2e^{x^2-y^2}ycos(2xy)-2e^{x^2-y^2}xsin(2xy)