Let f(x)= sin x, g(x)=x2 and h(x)= log e x If F ( x )=( hogof )( x ), then F ''( x ) is equal to

Question

Let f(x)= sin x, g(x)=x2 and h(x)= log e x If F ( x )=( hogof )( x ), then F ''( x ) is equal to (A) a cosec 3 x (B) 2 cot x2-4 x2 cosec 2 x2 (C) 2 x cot x2 (D) -2 cosec 2 x

Tardigrade Admin · Accepted Answer

Given, f(x)= sin x, g(x)=x2 and h(x)= log e x Also, F(x)=( hogof )(x)=( hog )( sin x)=h( sin x)2 ⇒ F ( x )=2 log sin x On differentiating, we get: F '( x )=2 cot x Again differentiating, we get: F ''( x )=-2 cosec 2 X

Q. Let $f (x) = sin x, g (x) = x^{2}$ and $h (x) = lo g_{e} x$
If $F (x) = ($ hogof $) (x)$ , then $F^{''} (x)$ is equal to

a $cosec^{3} x$

$2 cot x^{2} - 4 x^{2} cosec^{2} x^{2}$

$2 x cot x^{2}$

$- 2 cosec^{2} x$

Given, $f (x) = sin x, g (x) = x^{2}$ and $h (x) = lo g_{e} x$
Also, $F (x) = ($ hogof $) (x) = ($ hog $) (sin x) = h (sin x)^{2}$
$\Rightarrow F (x) = 2 lo g sin x$
On differentiating, we get: $F^{'} (x) = 2 cot x$
Again differentiating, we get: $F^{''} (x) = - 2 cosec^{2} X$

Q. Let f(x)=sinx,g(x)=x2 and h(x)=loge​x If F(x)=( hogof )(x), then F′′(x) is equal to

a cosec3x

2cotx2−4x2cosec2x2

2xcotx2

−2cosec2x