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