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h(x) = e^(sin^-1 x) or e^(cos^-1 x): find h'(x)/h(x)

The same question, asked 3 times: 4 May 2023 S2*, 9 May 2023 S2*, 10 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    135
    If f(x)=cos⁡−1x, g(x)=exf(x)=\cos^{-1}x,\, g(x)=e^x and h(x)=g(f(x))h(x)=g(f(x)), then h′(x)h(x)=\frac{h'(x)}{h(x)}=

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  2. Question 2

    9 May 2023 S2

    134
    Let f(x)=exf(x) = e^x, g(x)=sin⁡−1xg(x) = \sin^{-1}x and h(x)=f(g(x))h(x) = f(g(x)), then h′(x)h(x)2\frac{h'(x)}{h(x)^2} is equal to

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  3. Question 3

    10 May 2024 S1

    117
    f(x)=exf(x)=e^x, g(x)=sin⁡−1xg(x)=\sin^{-1}x, h(x)=f(g(x))h(x)=f(g(x)). Value of h′(x)h(x)\frac{h'(x)}{h(x)} is

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