What is (\partial)/(\partial x)(cos(x)*sin(y)) ?

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

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(\partial)/(\partial x)(cos(x)*sin(y))

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

- sin (x) sin (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

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

Simplify

= - sin (x) sin (y)

\int \frac{cot ^{4} ( x )}{csc ^{2} ( x )} d x

f (x) = 3 sin (2 x)

\frac{\partial}{\partial x} (4 x^{3} y + x y^{2})

- \frac{2 x}{( 4 + x ^{2} ) ^{2}}

x^{3} - 6 x^{2} - 34 x + 40, at x = 4

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