# What is the derivative of # y = 1/(secx- tanx)#?

Differentiate this using the quotient rule.

Hopefully this helps!

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( y = \frac{1}{\sec(x) - \tan(x)} ), use the quotient rule:

[ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \cdot u' - u \cdot v'}{v^2} ]

Where ( u = 1 ) and ( v = \sec(x) - \tan(x) ). Differentiate ( u ) and ( v ) with respect to ( x ), then apply the quotient rule. The derivative is:

[ y' = \frac{(\sec(x) - \tan(x)) \cdot (0) - (1) \cdot (\sec(x)\tan(x) + \sec^2(x))}{(\sec(x) - \tan(x))^2} ]

Simplify to get the final derivative:

[ y' = -\frac{\sec(x)\tan(x) + \sec^2(x)}{(\sec(x) - \tan(x))^2} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7