Question

y=e^sin√x....... dy/dx​

Answer 1

Apply chain rule

Differentiate in terms of sin√x, then in terms of √x and then in terms of x.

Derivatives used

• d(eˣ)/dx = eˣ

• d(sin(x))/dx = cos(x)

• d(xⁿ)/dx = nxⁿ⁻¹

Answer 2

Derivatives used :-

• { e^[a(x)] }' = e^[a(x)] . a(x)
• [sin a(x) ]' = cos a(x) . a'(x)
• (a^n)' = n . a^(n - 1)

The final answer is :-

$\sf{\dfrac{\cos\left(\sqrt{x}\right)\mathrm{e}^{\sin\left(\sqrt{x}\right)}}{2\sqrt{x}}}$