What is (\partial)/(\partial y)(sin(x)cos(7y)) ?

The answer to (\partial)/(\partial y)(sin(x)cos(7y)) is -7sin(x)sin(7y)

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(\partial)/(\partial y)(sin(x)cos(7y))

\frac{\partial}{\partial y} (sin (x) cos (7 y))

- 7 sin (x) sin (7 y)

Solution steps

\frac{\partial}{\partial y} (sin (x) cos (7 y))

Treat

x

as a constant

Take the constant out:

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

= sin (x) \frac{\partial}{\partial y} (cos (7 y))

Apply the chain rule:

- sin (7 y) \frac{\partial}{\partial y} (7 y)

= - sin (7 y) \frac{\partial}{\partial y} (7 y)

\frac{\partial}{\partial y} (7 y) = 7

= sin (x) (- sin (7 y) \cdot 7)

Simplify

= - 7 sin (x) sin (7 y)

\frac{\partial}{\partial u} (\frac{u - v}{2})

\frac{\partial}{\partial x} (5 x + y)

\int \frac{7 x ^{2}}{1 - x ^{6}} d x

\frac{d}{d y} (y z)

x \to 2 lim (- x^{2} + 3)

What is (\partial)/(\partial y)(sin(x)cos(7y)) ?
The answer to (\partial)/(\partial y)(sin(x)cos(7y)) is -7sin(x)sin(7y)