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Popular >

derivative of xcos(y-x)

Solution

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

Solution

cos (y - x) - x sin (y - x) (\frac{d y}{d x} - 1)

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (y - x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (y - x)) = - sin (y - x) (\frac{d y}{d x} - 1)

= 1 \cdot cos (y - x) + (- sin (y - x) (\frac{d y}{d x} - 1)) x

Simplify

= cos (y - x) - x sin (y - x) (\frac{d y}{d x} - 1)

Popular Examples

integral of cos(4x+5)

\int cos (4 x + 5) d x

integral of ((2x)/(x^2-36)+1/x+7)

\int (\frac{2 x}{x ^{2} - 36} + \frac{1}{x} + 7) d x

\int c

(dy)/(dx)=-3y^{2/3}sin(x)

\frac{d y}{d x} = - 3 y^{\frac{2}{3}} sin (x)

limit as x approaches-infinity of 3/x

x \to - \infty lim (\frac{3}{x})

Frequently Asked Questions (FAQ)

What is the derivative of xcos(y-x) ?
The derivative of xcos(y-x) is cos(y-x)-xsin(y-x)((dy)/(dx)-1)
What is the first derivative of xcos(y-x) ?
The first derivative of xcos(y-x) is cos(y-x)-xsin(y-x)((dy)/(dx)-1)