What is (\partial)/(\partial x)(sin(x)-cos(xy)) ?

The answer to (\partial)/(\partial x)(sin(x)-cos(xy)) is cos(x)+ysin(xy)

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(\partial)/(\partial x)(sin(x)-cos(xy))

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

cos (x) + y sin (x y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (x) - (- sin (x y) y)

Simplify

= cos (x) + y sin (x y)

\frac{\partial}{\partial x} (63 x^{3} cos (9 x^{2} y))

f (x) = - 8 cos (2 x)

\int_{- 3}^{3} (9 - x^{2}) d x

\int \frac{169 - x ^{2}}{x} d x

\frac{d}{d x} (\frac{( x - 1 )}{( x + 1 )})

What is (\partial)/(\partial x)(sin(x)-cos(xy)) ?
The answer to (\partial)/(\partial x)(sin(x)-cos(xy)) is cos(x)+ysin(xy)