Find the second derivate of :
(i) x11 (ii) 5x
(iii) tan x (iv) cos-1x
(i) x11
Differentiating with respect to x
f’(x) = 11x11-1
f’(x)=11x10
Differentiating with respect to x
f’’(x) = 110x10-1
f’’(x)= 110x9
(ii) 5x
Differentiating with respect to x
f’(x)= 5x loge 5 [ Formula: ax = ax logea ]
Differentiating with respect to x
f’’(x)= loge5 . 5x loge5
= 5x(loge5)2
(iii) tan x
Differentiating with respect to x
f’(x)= sec2x
Differentiating with respect to x
f’’(x)= 2secx . secx tanx
= 2sec2x tanx
(iv) cos-1x
Differentiating with respect to x
Differentiating with respect to x
=