We know the derivative of e^{x}, which is e^{x}.
(e^{x})' = e^{x}
We can find the derivative of e^{√cosx} using chain rule.
Find ᵈʸ⁄dₓ, if
y = e^{√cosx}
Let u = cosx.
y = e^{√u}
Let v = √u.
y = e^{v}
Now,
y = e^{v} ----> y is a function of v
v = √u ----> v is is a function of u
u = cosx ----> u is is a function of x
By chain rule, the derivative of y with respect to x :
Substitute y = e^{v}, v = √u and u = cosx.
Substitute v = √u.
Substitute u = cosx.
Therefore,
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