What is the derivative of ycos(xy) ?

The derivative of ycos(xy) is cos(xy)(dy)/(dx)-sin(xy)(y+x(dy)/(dx))y

What is the first derivative of ycos(xy) ?

The first derivative of ycos(xy) is cos(xy)(dy)/(dx)-sin(xy)(y+x(dy)/(dx))y

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = cos (x y)

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

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

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

Simplify

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

5 x^{2}, x^{2} + 4

x^{2} y^{^{'}} + x y = 8

\frac{\partial}{\partial x} (4 x y + 3)

\int x cos (\frac{π x}{2}) d x

\int_{1}^{2} \frac{1}{2 x + 1} d x

What is the derivative of ycos(xy) ?
The derivative of ycos(xy) is cos(xy)(dy)/(dx)-sin(xy)(y+x(dy)/(dx))y
What is the first derivative of ycos(xy) ?
The first derivative of ycos(xy) is cos(xy)(dy)/(dx)-sin(xy)(y+x(dy)/(dx))y