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

The answer to (\partial)/(\partial x)(cos(x)sin(x)-xy) is cos(2x)-y

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

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

cos (2 x) - y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (cos (x) sin (x)) = cos (2 x)

\frac{\partial}{\partial x} (x y) = y

= cos (2 x) - y

\frac{\partial}{\partial x} (4)

a x + b

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

\int tan (5 v) sec (5 v) d v

\frac{d y}{d t} = 20 - \frac{y}{230 + t}

What is (\partial)/(\partial x)(cos(x)sin(x)-xy) ?
The answer to (\partial)/(\partial x)(cos(x)sin(x)-xy) is cos(2x)-y