# How do you differentiate #f(x)=cos(3x)*(-2/3sinx)# using the product rule?

The following guidelines must be followed in order to answer this question:

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

To differentiate the function ( f(x) = \cos(3x) \left(-\frac{2}{3}\sin(x)\right) ) using the product rule:

Let ( u(x) = \cos(3x) ) and ( v(x) = -\frac{2}{3}\sin(x) ).

Then, ( u'(x) = -3\sin(3x) ) and ( v'(x) = -\frac{2}{3}\cos(x) ).

Applying the product rule:

[ f'(x) = u(x)v'(x) + v(x)u'(x) ]

[ = (\cos(3x))\left(-\frac{2}{3}\cos(x)\right) + \left(-\frac{2}{3}\sin(x)\right)(-3\sin(3x)) ]

[ = -\frac{2}{3}\cos(3x)\cos(x) + 2\sin(x)\sin(3x) ]

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 find the derivative of the function: #f(x) = x^3 - 3x^2 - 1#?
- What is the derivative of #ln e^(2x)#?
- How do you find the derivative of #y = 6 cos(x^3 + 3)# using the chain rule?
- What is the first and second derivative of #y = x^4 - 6x^2 + 8x + 8 #?
- What is the first differential of #y= e^sinsqrtx# ?

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