Question

Find the second derivate of :

(i) x¹¹

(ii) 5^x

(iii) tan x

(iv) cos^-1x

Answer 1

(i) x¹¹

Differentiating with respect to x

f’(x) = 11x^{11 - 1}

f’(x)=11x¹⁰

Differentiating with respect to x

f’’(x) = 110x^10-1

f’’(x)= 110x⁹

(ii) 5^x

Differentiating with respect to x

f’(x)= 5^x log_e 5 [ Formula: a^x = a^x loge^a ]

Differentiating with respect to x

f’’(x)= log_e5 . 5x log_e5

= 5x(log_e5)²

(iii) tan x

Differentiating with respect to x

f’(x)= sec²x

Differentiating with respect to x

f’’(x)= 2secx . sec x tan x = 2sec 2x tan x

(iv) cos^-1x Differentiating with respect to x

Differentiating with respect to x