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Differentiate the following with respect...

Differentiate the following with respect to x.
(i) `x^6` (ii) `(1)/(x^3)` (iii) `sqrtx`

A

`6x^4` , `(-3)/(x^4)` , `(1)/(2sqrtx)`

B

`6x^5` , `(-3)/(x^4)` , `(1)/(2sqrtx)`

C

`6x^5` , `(-2)/(x^4)` , `(1)/(2sqrtx)`

D

`6x^3` , `(-3)/(x^4)` , `(1)/(2sqrtx)`

Text Solution

Verified by Experts

The correct Answer is:
B
(i) `y = x^6 , (dy)/(dx) = 6x^(6-1) = 6x^5` (ii) `y = (1)/(x^3) = x^(-3) , (dy)/(dx) = (-3)x^(-3-1) = -3x^(-4) = (-3)/(x^4)`
(iii) `y = sqrtx = x^(1/2) , (dy)/(dx) = (1)/(2) x ^(((1)/(2)-1)) = (1)/(2)x ^(-(1)/(2)) = (1)/(2sqrtx)`
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