Q. 14.3( 3 Votes )

Find the second derivate of :

(i) x11 (ii) 5x

(iii) tan x (iv) cos-1x

Answer :

(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



=


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