# How do you find the derivative of # (3+sin(x))/(3x+cos(x))#?

Use quotient rule to obtain

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

To find the derivative of ( \frac{3+\sin(x)}{3x+\cos(x)} ), you can use the quotient rule, which states that for functions ( u(x) ) and ( v(x) ), the derivative of ( \frac{u(x)}{v(x)} ) is given by ( \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ). Applying this rule to the given function, the derivative is:

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

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

[ = \frac{9 - \sin^2(x) - 9x\cos(x) - 3\sin(x) - 3\cos(x) - x\cos^2(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