That's not right. The answer shouldn't be ln5/5, because that's a number. The answer should be a function.chanella35 said:the question is: differentiate wiith repsect to x:
(ln(5x))^1/5
i differentiated and got :
1/5ln(5x)
y'=1/5xI don't think this is correct. The answer should be ln5/5.
Can anyone help me?
chanella
logarithmic said:That's not right. The answer shouldn't be ln5/5, because that's a number. The answer should be a function.
Use the chain rule: power to the front, subtract 1, multiply by the derivative of what's inside the bracket.
chanella35 said:So the answer would be;
y'=1/5 (5)(ln5x)^(1/5-1)
y'= (ln5x)^-4/5
is this right??
Thanks for helping :)
The formula for differentiating natural logs (ln) is d/dx(ln(x)) = 1/x. This means that the derivative of ln(x) is equal to 1 divided by x.
Yes, the derivative of ln(x) is the same as the derivative of log base e (e), since ln(x) and log base e (e) are just different notations for the same mathematical function.
No, natural logs (ln) cannot be differentiated using the power rule. The power rule only applies to functions in the form of x^n, while ln(x) is a logarithmic function.
The derivative of ln(e^x) is simply 1, since e^x is the inverse function of ln(x) and their derivatives cancel each other out.
The chain rule can be used to differentiate natural logs (ln) by first taking the derivative of the inside function, then multiplying it by the derivative of the outside function. For example, to differentiate ln(3x), the chain rule would be used as d/dx(ln(3x)) = (1/3x) * (3) = 1/x.