Question

Suppose L is a function such that L'(x)=1/x for x>0. Find an expression for the derivative of g(x)=L(7 x)

Answer 1

The derivative of g(x)=L(7x) is 1/x.

Step-by-step explanation:

To find the derivative of g(x)=L(7x), we can use the chain rule. First, let's find the derivative of L(x). Given that L'(x)=1/x for x>0, we can see that L(x) must be the natural logarithm function, ln(x).

Now, to find the derivative of g(x)=L(7x), we substitute 7x into the function L(x) and differentiate with respect to x.

So, g'(x)=L'(7x) * 7 = (1/(7x)) * 7 = 1/x.