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Popular >

d/(dy)(ycos(xy))

Solution

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

Solution

cos (y x) - y x sin (y x)

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = y, g = cos (x y)

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

\frac{d y}{d y} = 1

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

= 1 \cdot cos (x y) + (- sin (x y) x) y

Simplify

= cos (y x) - y x sin (y x)

Popular Examples

sum from n=1 to infinity of 5*3^n

n = 1 \sum \infty 5 \cdot 3^{n}

(\partial)/(\partial y)(-2sin(y)+xy^3)

\frac{\partial}{\partial y} (- 2 sin (y) + x y^{3})

integral of 1/((225+x^2)^{3/2)}

\int \frac{1}{( 225 + x ^{2} ) ^{\frac{3}{2}}} d x

integral of e^x(3e^x-2)^2

\int e^{x} (3 e^{x} - 2)^{2} d x

derivative of ln(8x+7)

\frac{d}{d x} (ln (8 x + 7))

Frequently Asked Questions (FAQ)

What is the d/(dy)(ycos(xy)) ?
The d/(dy)(ycos(xy)) is cos(yx)-yxsin(yx)
What is the first d/(dy)(ycos(xy)) ?
The first d/(dy)(ycos(xy)) is cos(yx)-yxsin(yx)