# How do I differentiate #y= sec^2(x) + tan^2(x)#?

Use the chain rule (generalized power rule) and the derivatives of the trigonometric functions. Beyond that, there are choices you can make

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

To differentiate ( y = \sec^2(x) + \tan^2(x) ), use the chain rule for differentiation:

[ \frac{d}{dx} \left( \sec^2(x) + \tan^2(x) \right) = \frac{d}{dx} \sec^2(x) + \frac{d}{dx} \tan^2(x) ]

Apply the derivative formulas for ( \sec^2(x) ) and ( \tan^2(x) ):

[ \frac{d}{dx} \sec^2(x) = 2\sec(x) \tan(x) \sec(x) = 2\sec(x) \tan(x) ]

[ \frac{d}{dx} \tan^2(x) = 2\tan(x) \sec^2(x) ]

Substitute these derivatives back into the original expression:

[ \frac{d}{dx} \left( \sec^2(x) + \tan^2(x) \right) = 2\sec(x) \tan(x) + 2\tan(x) \sec^2(x) ]

[ = 2\sec(x) \tan(x) + 2\tan(x) \sec^2(x) ]

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