Question

Find the derivative by first principle:
$\rm x\sqrt{x}$

Answer 1

HOPE IT HELPS U ✌️✌️✌️

Answer 2

Answer:

3√x / 2

Step-by-step explanation:

f(x)  = x√x

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

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

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

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

=> f'(x)  =   Lim h- 0    (( x + h)³  - x³)/(h(( x + h)√(x + h)  + x√x))

=> f'(x)  =   Lim h- 0    (h³ + 3x²h + 3xh²)/(h(( x + h)√(x + h)  + x√x))

=> f'(x)  =   Lim h- 0    (h² + 3x² + 3xh)/(( x + h)√(x + h)  + x√x))

putting h = 0

=>  f'(x)  = 3x² / 2 x√x

=> f'(x)  = 3√x / 2