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Popular >

derivative of xsin(xy)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = sin (x y)

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

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

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

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

Simplify

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

Popular Examples

limit as t approaches infinity of cos(t)

t \to \infty lim (cos (t))

(dy}{dt}=\frac{3y)/t+t^5

\frac{d y}{d t} = \frac{3 y}{t} + t^{5}

limit as x approaches c of f(x)

x \to c lim (f (x))

derivative of-2*x*e^{-x^2}

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

integral of 1/(xsqrt(196x^2-196))

\int \frac{1}{x 196 x ^{2} - 196} d x

Frequently Asked Questions (FAQ)

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