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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