Let f(.x.)=ex,g(.x.)=(sin)- 1x and h(.x.)=f(.g(.x.).) then h'(.x.)/h(.x.)=

Question

Let f(.x.)=ex,g(.x.)=(sin)- 1x and h(.x.)=f(.g(.x.).) then h'(.x.)/h(.x.)= (A) esin- 1 x (B) 1/√1 - x2 (C) sin- 1x (D) 1/(1 - x2)

Tardigrade Admin · Accepted Answer

f ( x )= e x and g ( x )= sin -1 x and h ( x )= f ( g ( x )) ⇒ h ( x )= f ( sin -1 x )= c sin -1 x ⇒ h ( x )=( e sin -1 x /√1- x 2) ⇒ ( h ( x )/ h ( x ))=(1/√1- x 2)

Q. Let $f (x) = e^{x}, g (x) = (s in)^{- 1} x$ and $h (x) = f (g (x))$ then $h^{^{'}} (x) / h (x) =$

$e^{s i n^{- 1} x}$

$1/ 1 - x^{2}$

$s i n^{- 1} x$

$1/ (1 - x^{2})$

$f (x) = e^{x}$ and $g (x) = sin^{- 1} x$ and $h (x) = f (g (x))$
$\Rightarrow h (x) = f (sin^{- 1} x) = c^{s i n^{- 1} x}$
$\Rightarrow h (x) = \frac{e ^{s i n^{- 1} x}}{1 - x ^{2}}$
$\Rightarrow \frac{h ( x )}{h ( x )} = \frac{1}{1 - x ^{2}}$

Q. Let f(x)=ex,g(x)=(sin)−1x and h(x)=f(g(x)) then h′(x)/h(x)=

esin−1x

1/1−x2​

sin−1x

1/(1−x2)