How do you differentiate #(x)/ (1-cosx)# using the quotient rule?
The quotient rule states that
We can find each of the internal derivatives and then plug them back in:
Plugging it all back in:
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate the function ( \frac{x}{1-\cos(x)} ) using the quotient rule:
- Let ( u = x ) and ( v = 1 - \cos(x) ).
- Apply the quotient rule: [ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} ]
- Compute ( \frac{du}{dx} ) and ( \frac{dv}{dx} ). [ \frac{du}{dx} = 1 ] [ \frac{dv}{dx} = \sin(x) ]
- Substitute the values into the quotient rule formula: [ \frac{d}{dx} \left( \frac{x}{1-\cos(x)} \right) = \frac{(1-\cos(x))(1) - (x)(\sin(x))}{(1-\cos(x))^2} ]
- Simplify the expression if necessary.
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.
- How do you differentiate #f(x)=x/(1+sqrtx)#?
- How do you differentiate #x^3 yz^2+w^2 x^2 y-x^3+wsiny=44#?
- How do you use the power rule to differentiate #f(x)=3x^5+2/sqrtx#?
- How do you differentiate #f(x) = 4/sqrt(tan^3(1/x) # using the chain rule?
- How do you differentiate #f(x)=(2x+3)^4 / x# using the chain rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7