Question

Que f(x+h)-f(x) Compute the difference quotient, for the function f(x) = 5x², and simplify. h f(x+h) -f(x) h (Simplify your answer.)

Answer 1

`f'(x)=10x`

Explanation:

`\displaystyle f'(x)=\lim_(h\rightarrow0)(f(x+h)-f(x))/(h)\\\\f'(x)=\lim_(h\rightarrow0)(5(x+h)^2-5x^2)/(h)\\\\f'(x)=\lim_(h\rightarrow0)(5(x^2+2xh+h^2)-5x^2)/(h)\\\\f'(x)=\lim_(h\rightarrow0)(5x^2+10xh+5h^2-5x^2)/(h)\\\\f'(x)=\lim_(h\rightarrow0)(10xh+5h^2)/(h)\\\\f'(x)=\lim_(h\rightarrow0)10x+5h\\\\f'(x)=10x+5(0)\\\\f'(x)=10x`