# How do you differentiate #f(x)=sin^2x/cos^2x#?

Hopefully this helps!

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

To differentiate ( f(x) = \frac{\sin^2(x)}{\cos^2(x)} ), you can use the quotient rule. The quotient rule states that if you have a function ( \frac{u(x)}{v(x)} ), then its derivative is given by ( \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} ). Applying this rule to the function ( f(x) ), where ( u(x) = \sin^2(x) ) and ( v(x) = \cos^2(x) ), we get:

[ f'(x) = \frac{(2\sin(x)\cos(x))( \cos^2(x)) - (\sin^2(x))(2\cos(x)(-\sin(x)))}{[\cos^2(x)]^2} ]

Simplify the expression:

[ f'(x) = \frac{2\sin(x)\cos^3(x) - 2\sin^2(x)\cos(x)}{\cos^4(x)} ]

[ f'(x) = \frac{2\sin(x)\cos(x)(\cos^2(x) - \sin^2(x))}{\cos^4(x)} ]

[ f'(x) = \frac{2\sin(x)\cos(x)\cos(2x)}{\cos^4(x)} ]

[ f'(x) = \frac{2\sin(x)\cos(2x)}{\cos^3(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