What is (\partial)/(\partial y)(e^{cos(x-2y)}) ?

The answer to (\partial)/(\partial y)(e^{cos(x-2y)}) is e^{cos(x-2y)}*2sin(x-2y)

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(\partial)/(\partial y)(e^{cos(x-2y)})

\frac{\partial}{\partial y} (e^{c o s (x - 2 y)})

e^{c o s (x - 2 y)} \cdot 2 sin (x - 2 y)

Solution steps

\frac{\partial}{\partial y} (e^{c o s (x - 2 y)})

Treat

x

as a constant

Apply the chain rule:

e^{c o s (x - 2 y)} \frac{\partial}{\partial y} (cos (x - 2 y))

= e^{c o s (x - 2 y)} \frac{\partial}{\partial y} (cos (x - 2 y))

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

= e^{c o s (x - 2 y)} \cdot 2 sin (x - 2 y)

\frac{d}{d x} (ln (1 - 8 x))

x \frac{d y}{d x} - y = 3 x^{4}

\frac{d}{d x} ((- 3 x + 1)^{3} (2 x - 1)^{4})

What is (\partial)/(\partial y)(e^{cos(x-2y)}) ?
The answer to (\partial)/(\partial y)(e^{cos(x-2y)}) is e^{cos(x-2y)}*2sin(x-2y)