What is (\partial)/(\partial x)(e^xcos(xy)) ?

The answer to (\partial)/(\partial x)(e^xcos(xy)) is e^xcos(xy)-e^xysin(xy)

Popular >

(\partial)/(\partial x)(e^xcos(xy))

\frac{\partial}{\partial x} (e^{x} cos (x y))

e^{x} cos (x y) - e^{x} y sin (x y)

Solution steps

\frac{\partial}{\partial x} (e^{x} cos (x y))

Treat

y

as a constant

Apply the Product Rule:

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

f = e^{x}, g = cos (x y)

= \frac{\partial}{\partial x} (e^{x}) cos (x y) + \frac{\partial}{\partial x} (cos (x y)) e^{x}

\frac{\partial}{\partial x} (e^{x}) = e^{x}

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

= e^{x} cos (x y) + (- sin (x y) y) e^{x}

Simplify

= e^{x} cos (x y) - e^{x} y sin (x y)

\int_{1}^{6} f (\frac{1}{2} x) d x

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

y^{^{'}} = x - x y

\int e^{s i n (t)} d t

(1.1) (4.2)

What is (\partial)/(\partial x)(e^xcos(xy)) ?
The answer to (\partial)/(\partial x)(e^xcos(xy)) is e^xcos(xy)-e^xysin(xy)