Question

differentiate using limit sqrt (x+9)

Answer 1

do you mean using the limit definition of a derivative?

Answer 2

\[\lim_{h\to 0}\frac{\sqrt{x+h+9}-\sqrt{x+9}}{h}\] multiply top and bottom by the conjugate of the numerator
\[\lim_{h\to 0}\frac{\sqrt{x+h+9}-\sqrt{x+9}}{h}\times\frac{\sqrt{x+h+9}+\sqrt{x+9}}{\sqrt{x+h+9}+\sqrt{x+9}}\]

Answer 3

leave the denomiator in factored form. the numerator will just be \(h\)
cancel the \(h\) top and bottom, then replace \(h\) by 0

Answer 4

so after the conjugate multiplying in, it would be x+h+9 - x -9 / h(the sqrt plus the other sqrt) right?

Answer 5

so 1/ the sqrt + the sqrt

Answer 6

got it thanks