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

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

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(\partial)/(\partial x)(cos(x^2-y))

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

- sin (x^{2} - y) \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= - sin (x^{2} - y) \cdot 2 x

\int \frac{2 x}{x - 1} d x

\frac{\partial}{\partial y} (3 y)

4 y^{^{''}} - 4 y^{^{'}} + 4 y = 0

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

x^{^{''}} + 9 x - 27 = 0, x (0) = 4, x^{^{'}} (0) = 6

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