Question

Find the derivative by first principle:
$\rm \frac{1}{2x+3}$

Answer 1

HOPE IT HELPS U ✌️✌️

Answer 2

Answer:

-2/ (2x + 3)²

Step-by-step explanation:

f(x)  = 1/(2x + 3)

f'(x)  = Lim h-0   (f(x+h) - f(x) )/ h

=> f'(x)  = Lim h-0   ((1/(2x + 2h + 3)  - 1/(2x + 3) )/ h

=> f'(x)  = Lim h-0   (2x + 3 - (2x + 2h + 3))/( h(2x + 3)(2x + 2h + 3))

=> f'(x)  = Lim h-0   (- 2h)/( h(2x + 3)(2x + 2h + 3))

=> f'(x)  = Lim h-0   (- 2)/(2x + 3)(2x + 2h + 3)

puttinh h = 0

=>  f'(x)  = -2/ (2x + 3)²