Question

differentiate from first principles
2x^3 -5
(f(x+h)-f(x))/h

i know what it should be but i keep going wrong somewhere

thanks

Answer 1

f(x+h)= 2(x+h)^3-5
= 2(x^3+3hx^2+3xh^2+ h^3

let me check the coefficents
121
1331
If you don't recognize, that see Pascal's triangle)
Now subtract f(x) from that, or
2(3hx^2+3xh^2+h^3)
divide by h
2(3x^2+3hx+h^2)
now take the lim h>zero
6x^2