# How do you differentiate #f(x)=sin2x * cot(5-x)# using the product rule?

When separating a product of two functions, the rule to follow is

Thus

where the standard rules have been applied

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

The derivative of

According to the product rule,

Having established the rules, let's calculate the derivative.

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

To differentiate ( f(x) = \sin(2x) \cdot \cot(5-x) ) using the product rule:

[ f'(x) = (\sin(2x))' \cdot \cot(5-x) + \sin(2x) \cdot (\cot(5-x))' ]

Apply the chain rule and derivative of cotangent:

[ f'(x) = (2\cos(2x)) \cdot \cot(5-x) + \sin(2x) \cdot \left( -\csc^2(5-x) \right) ]

So, the derivative of ( f(x) = \sin(2x) \cdot \cot(5-x) ) using the product rule is:

[ f'(x) = 2\cos(2x) \cdot \cot(5-x) - \sin(2x) \cdot \csc^2(5-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.

- How do you differentiate # y = sin (x^2+2)# using the chain rule?
- How do you find the derivative of #G(x) = sqrtx (x^2 – x)^3#?
- How do you differentiate #f(x)= (x-e^(x))/(e^x-3x)# using the quotient rule?
- How do you differentiate #y=x^-2cosx-4x^-3#?
- How do you differentiate # y =sqrtln(x^2-3x)# 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