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Find (dy)/(dx), when (i) y=sqrt(x) (ii...

Find (dy)/(dx), when
(i) `y=sqrt(x)` (ii) `y=x^(5)+x^(4)+7` (iii) `y=x^(2)+4x^(-1//2)-3x^(-2)`

Text Solution

Verified by Experts

(i) `y= sqrtx rArr" "(dy)/(dx) = (d)/(dx) (sqrtx) = (d)/(dx) (x^(1//2))= (1)/(2) x^((1)/(2)-1)= (1)/(2) x^(-1//2) = (1)/(2sqrtx)`
(ii) `y= x^(5) + x^(4) + 7 " "rArr (dy)/(dx)=(d)/(dx) (x^(5) + x^(4) +7) = (d)/(dx) (x^(5)) + (d)/(dx) (x^(4)) + (d)/(dx) (7)`
(iii) `y= x^(2) + 4x^(-1//2) - 3x^(-2) rArr (dy)/(dx)= (d)/(dx)(x^(2) +4x^(-1//2) - 3x^(-2)) = (d)/(dx) (x^(2))+ (d)/(dx) (4x^(-1//2) - (d)/(dx)(3x^(-2))`
`" "= (d)/(dx) (x^(2)) + 4(d)/(dx) (x^(-1//2)-3(d)/(dx)(x^(-2))=2x + 4 (-(1)/(2))=2x + 4 (-(1)/(2))x^(-3//2) -3 (-2)x^(-3)`
`" "= 2x-2x^(-3//2) + 6x^(-3)`
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