6/ln[x]
find the derivative...
im coming up with -6/x*(ln(x))^2
but it isn't accepting the answer
what am i doing wrong?
nevermind it won't accept ANY answer now so it doesn't matter
Your answer is actually correct. :)
d/dx (6/ln(x))
d/dx (6*(ln(x))^(-1))
= 6(-1)(1/x)(ln(x))^2
= -6/(x*(ln(x))^2)
To find the derivative of 6/ln(x), you need to apply the quotient rule. The quotient rule states that if you have a function in the form of f(x)/g(x), where f(x) and g(x) are both functions, then the derivative is given by:
(f'(x) * g(x) - g'(x) * f(x)) / (g(x))^2
In this case, let f(x) = 6 and g(x) = ln(x). Applying the quotient rule, we have:
f'(x) = 0 (the derivative of a constant is always zero)
g'(x) = 1/x (the derivative of ln(x) is 1/x)
Plugging these values into the quotient rule formula, we get:
(0 * ln(x) - 1/x * 6) / (ln(x))^2
= (-6/x) / (ln(x))^2
= -6/(x * (ln(x))^2)
So, your derivative is indeed -6/(x * (ln(x))^2).
If your answer is not being accepted, make sure that you have simplified it correctly. Some common ways to simplify this expression further are:
Option 1: Move the negative sign to the numerator:
-6/(x * (ln(x))^2) = -6/(x * ln(x))^2
Option 2: Expand the square in the denominator:
-6/(x * (ln(x))^2) = -6/(x * ln(x) * ln(x))
Try both of these simplifications and see if either of them matches the expected answer.