# How do you implicitly differentiate #-3=xsecy#?

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To implicitly differentiate -3 = xsec(y) with respect to x, follow these steps:

- Differentiate both sides of the equation with respect to x.
- Apply the chain rule where necessary.
- Solve for dy/dx, which represents the derivative of y with respect to x.

Here are the steps:

-3 = xsec(y)

Differentiate both sides with respect to x:

0 = d/dx(xsec(y))

Apply the chain rule:

0 = sec(y) * (d(x)/dx) + x * d(sec(y))/dx

Using the derivatives of sec(y) and sec(y)tan(y):

0 = sec(y) * (1) + x * (sec(y)tan(y) * (dy/dx))

Rearrange the equation to solve for dy/dx:

dy/dx = -sec(y)/x * tan(y)

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