Question

Use the alternate definition of derivative to find the derivative.Question: f(x)=3x^2+x

Answer 1

`f^(\prime)(a)=\lim _(x\to a)(f(x)-f(a))/(x-a)`

Procedure:

0. Reeplacing the function

`f^(\prime)(a)=\lim _(x\to a)((3x^2+x)-(3a^2+a))/(x-a)`
`f^(\prime)(a)=\lim _(x\to a)\frac{x(3x+1)-a(3a^{}+1)}{x-a}`
`f^(\prime)(a)=\lim _(x\to a)(-(x-a)(-3x-3a-1))/(x-a)`
`f^(\prime)(a)=\lim _(x\to a)(3x+3a+1)`
`f^(\prime)(a)=3a+3a+1`

Answer:

`f^(\prime)(a)=6a+1`