# How do you use the chain rule to differentiate #y=(cosx/(1+sinx))^5#?

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

To differentiate ( y = \left(\frac{\cos x}{1 + \sin x}\right)^5 ) using the chain rule, follow these steps:

- Let ( u = \frac{\cos x}{1 + \sin x} ).
- Find ( \frac{du}{dx} ) by differentiating ( u ) with respect to ( x ).
- Apply the chain rule: ( \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} ).
- Differentiate ( y ) with respect to ( u ) to find ( \frac{dy}{du} ).
- Substitute the expressions for ( \frac{dy}{du} ) and ( \frac{du}{dx} ) back into ( \frac{dy}{dx} ) to get the final derivative.

The result is ( \frac{dy}{dx} = -5\sin x(\cos x + 1)^4 ).

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