Question

Find f(x) if f'(x)= (2x+sqrt(x))/(x), f(1)=3

step by step.. I don't know how to solve these

Answer 1

@zepdrix desperate need of help D;

Answer 2

Are you familiar with the integral notation yet? :D

Answer 3

not at all D; and my exam is in 3 hours... uhhh oh

Answer 4

Breaking up the fractions will help us a little bit.\[\huge \frac{2x+\sqrt x}{x} \quad \rightarrow \quad \frac{2x}{x}+\frac{\sqrt x}{x}\]

Answer 5

\[\huge =2+\frac{1}{\sqrt x}\]Understand how that second term changed?
Keep in mind, this is STILL f'(x), we have NOT anti-differentiated yet.

Answer 6

wait how'd you go from 2x/x+sqrt(x)/x to 2+1/sqrt(x)

Answer 7

See where the 2 is coming from? x divided by x.

The other one is a little bit tricky.

Answer 8

\[\huge \frac{\sqrt x}{x}\qquad \rightarrow \qquad \frac{\sqrt x}{\sqrt x\cdot \sqrt x}\]

Answer 9

If the second term is giving you a lot of trouble, converting to fractional exponents might help.

Answer 10

I get the 2x/x part now.. not the sqt(x) is confusing me?

Answer 11

Try writing the X's with fractional exponents, does it make it a lil easier to understand? :O
You have to remember your rules of exponents though. When dividing, you SUBTRACT the exponents.