Calculus: Obtain the difference quotient for the function?

[chess127]

Can you please tell me how to obtain the difference quotient for the function f(x) = 5x^2-3x? Thank you. Is 10x + 5h - 3 the correct answer? How would you get to this answer?

 

[galactus]

\(\displaystyle \lim_{h\to 0}\frac{5(x+h)^{2}-2(x+5)-(5x^{2}-3x)}{h}\)

\(\displaystyle \lim_{h\to 0}\frac{10xh+5h^{2}-3h}{h}\)

\(\displaystyle \lim_{h\to 0}[10x+5h-3]\)

See?. Just as you have. Now, let h=0 and you have the derivative for 5x^2-3x

 

[chess127]

Thank you. That was very helpful.