Question

If f(x) = sinx, g(x) = x², h(x) = logx and F(x) = (hogof)(x), then F’’(x) is 

(A) 2cosec³x 

(B) 2cotx² − 4x²cosec²x² 

(C) 2xcotx² 

(D) − 2cosec²x

Answer 1

Answer is (D) − 2cosec²x

F(x) = (hogof)(x) = h{g[f(x)]}

= h[g(sinx)] = h(sin²x) = log_e(sin²x)

= 2loge(sinx)

There, F'(x) = 2cotx ⇒ F''(x) = - 2cosec²x