Please help with derivatives?

[natnat]

The problem:


a) Use the limit definition, of the derivative function to find f '(x) = df/dx if f(x)=(x-7)/3x+2


b) Give an equation to the normal line to f(x) at x=1



Thanks!



Please show your reasoning if you can


ADD. INFO; I was told to use the lim h-->0 f(x+h)-f(x)/h formula, but i'm still kind of stuck.. it gives me (x+h-7)/h(3x+3h+2)

 

[tkhunny]

The problem:


a) Use the limit definition, of the derivative function to find f '(x) = df/dx if f(x)=(x-7)/3x+2


b) Give an equation to the normal line to f(x) at x=1



Thanks!



Please show your reasoning if you can


ADD. INFO; I was told to use the lim h-->0 f(x+h)-f(x)/h formula, but i'm still kind of stuck.. it gives me (x+h-7)/h(3x+3h+2)

First, please fix your notation. This is NOT what you want: "f(x+h)-f(x)/h". How would you fix it?

Second, you should get: \(\displaystyle \dfrac{\dfrac{h+x-7}{3h+3x+2}-\dfrac{x-7}{3x+2}}{h} = \dfrac{23h}{(3x+2)(3h+3x+2)\cdot h}\)

 

[tkhunny]

THAT'S why my fractions are always so squishy! I get it. Special thanks to mmm4444bot!