# How do you differentiate #(3+sin(x))/(3x+cos(x))#?

You use the quotient rule.

Your function can be written as

You also need to remember that

and

Plug these values into the formula for the quotient product to get

Use the formula for the difference of two perfect squares to write

You can further simplify this expression by using the fact that

so that you get

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

To differentiate (3+sin(x))/(3x+cos(x)), you can use the quotient rule. The derivative is ((3*cos(x) - (3+sin(x))*(-3*sin(x) - cos(x)))/((3x+cos(x))^2).

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

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