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Popular >

derivative of xcos(xy)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x y)

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

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

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

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

Simplify

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

Popular Examples

integral from 6 to 8 of 1/((x-6)^3)

\int_{6}^{8} \frac{1}{( x - 6 ) ^{3}} d x

taylor 1/(1-2x)taylor

\frac{1}{1 - 2 x}

derivative of x/(2.4(c^2+cx)(c^2-x^2))

\frac{d}{d x} (\frac{x}{2.4 ( c ^{2} + c x )} (c^{2} - x^{2}))

integral of (cos(2t))/((1+sin(2t))^4)

\int \frac{cos ( 2 t )}{( 1 + sin ( 2 t ) ) ^{4}} d t

limit as x approaches-1 of (x+2)/(x^3+1)

x \to - 1 lim (\frac{x + 2}{x ^{3} + 1})

Frequently Asked Questions (FAQ)

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