Find the derivative of y with respect to x.
y= (lnx)/(3+4lnx)
Should I start by using the quotient rule?
You could, or...
y= (lnx)*1/(2+lnx)
y'= 1/x * 1/(2+lnx) - ln(x)/(2+lnx)^2 * 1/x
http://www.wolframalpha.com/widgets/view.jsp?id=bf1b2f4b901c21a1d8645018ea9aeb05
put
(lnx)/(3+4lnx)
in as your function
click on differentiate
click on "show steps"
Derivative:
Show steps
3/(x (4 log(x)+3)^2)
Yes, to find the derivative of the given function with respect to x, you can start by using the quotient rule. The quotient rule is a formula used to differentiate functions that are in the form of a quotient (one function divided by another).
The quotient rule states that if you have a function f(x) divided by g(x), where f(x) and g(x) are both differentiable functions, then the derivative of the quotient is given by the formula:
(f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2
In the case of y = (lnx) / (3 + 4lnx), you can identify f(x) = lnx and g(x) = (3 + 4lnx).
To find the derivative of f(x) = lnx, you can use the derivative of the natural logarithm function, which is 1/x.
To find the derivative of g(x) = (3 + 4lnx), you can use the sum rule and the derivative of lnx.
Now, you can differentiate f(x) and g(x) and substitute them into the quotient rule formula to find the derivative of y with respect to x.