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

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

To differentiate ( f(x) = \sin(2x) \cdot \cot(x) ) using the product rule, follow these steps:

- Identify the functions involved: ( u(x) = \sin(2x) ) and ( v(x) = \cot(x) ).
- Compute the derivatives of ( u(x) ) and ( v(x) ) with respect to ( x ): ( u'(x) = 2\cos(2x) ) and ( v'(x) = -\csc^2(x) ).
- Apply the product rule: ( f'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x) ).
- Substitute the derivatives and functions back into the formula: [ f'(x) = (2\cos(2x)) \cdot (\cot(x)) + (\sin(2x)) \cdot (-\csc^2(x)) ].
- Simplify the expression if necessary.

So, the derivative of ( f(x) = \sin(2x) \cdot \cot(x) ) using the product rule is: [ f'(x) = 2\cos(2x) \cdot \cot(x) - \sin(2x) \cdot \csc^2(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