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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{x + 1}{x - 1}

t^{5} ln ∣ t ∣

\frac{\partial}{\partial x} (lo g_{10} (x y))

y = x^{2} - 2 x, y = - x^{2} + 4 x

x \to 2 + lim (\frac{3}{x ^{2} - 4})

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