Let f ( x )= sin x ; g ( x )= x 2 h ( x )= log e x F ( x )= h [ g ( f ( x ))] then ( d 2 F / dx 2) is equal to -

Question

Let f ( x )= sin x ; g ( x )= x 2 h ( x )= log e x F ( x )= h [ g ( f ( x ))] then ( d 2 F / dx 2) is equal to - (A) 2 textcosec3 x (B) 2 cot (x2)-4 x2 textcosec2(x2) (C) 2 x cot x2 (D) -2 textcosec2 x

Tardigrade Admin · Accepted Answer

Correct answer is (d) -2 textcosec2 x

Q. Let $f (x) = sin x; g (x) = x^{2} & h (x) = lo g_{e} x & F (x) = h [g (f (x))]$ then $\frac{d ^{2} F}{d x ^{2}}$ is equal to -

$2 cosec^{3} x$

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

$2 x cot x^{2}$

$- 2 cosec^{2} x$

Correct answer is (d) $- 2 cosec^{2} x$

Q. Let f(x)=sinx;g(x)=x2&h(x)=loge​x&F(x)=h[g(f(x))] then dx2d2F​ is equal to -

2cosec3x

2cot(x2)−4x2cosec2(x2)

2xcotx2

−2cosec2x