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

The d/(dy)(e^{2y}-ycos(xy)) is 2e^{2y}-cos(yx)+yxsin(yx)

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

The first d/(dy)(e^{2y}-ycos(xy)) is 2e^{2y}-cos(yx)+yxsin(yx)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

e^{2 x}, 0

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

(x + 6) e^{3 x} + 4

\int 2^{x} sin (x) d x

x \to 2 lim (x^{2} + 3 x)

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