How do you find the derivative of #tan(x − y) = x#?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the derivative of ( \tan(x - y) = x ), you'll use implicit differentiation. First, differentiate both sides of the equation with respect to ( x ), treating ( y ) as a function of ( x ). Then, solve for ( \frac{dy}{dx} ).
The derivative of ( \tan(x - y) ) with respect to ( x ) is ( \sec^2(x - y) \frac{d}{dx}(x - y) ).
Applying the chain rule to ( \frac{d}{dx}(x - y) ), we get ( 1 - \frac{dy}{dx} ).
Setting this equal to ( 1 ) (the derivative of ( x )), we have ( \sec^2(x - y)(1 - \frac{dy}{dx}) = 1 ).
Rearranging and solving for ( \frac{dy}{dx} ), we get ( \frac{dy}{dx} = 1 - \sec^2(x - y) ).
Therefore, the derivative of ( \tan(x - y) = x ) with respect to ( x ) is ( \frac{dy}{dx} = 1 - \sec^2(x - y) ).
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.
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