Question

Please help me solve m(x)=ln(2x+1)

Answer 1

This just a chain rule problem

The main thing about the chain rule is that the derivative of the whole thing is the derivative of the outside function times the derivative of the inside function. So

The outside function is ln(inside function) and the inside function is 2x + 1.

m'(x) = (ln(2x+1)' = ln'(2x+1)(2x+1)'

Answer 2

And how to sketch the graph?

Answer 3

You mean m(x) or its derivative?

About m(x): ln is a swoop from deep negative near the negative y axis to slowly increasing positive in the first quadrant -- But the +1 has the effect of slipping everything to the left.. ln(x) would cross the x axis at 1 and have no values for negative x. So 2x would cross the x axis at 1/2, and still have no value for negative x. But the +1 gives you a cushion so x can have negative values of upto -1/2. You should see that when x = 0 m(x) becomes ln(1/1), and ln 1 is 0, so the graph goes through the origin. .

Answer 4

something like this la?