How do you differentiate #f(x)=sqrtsin(e^(4x))# using the chain rule.?
1 Answer
Feb 9, 2016
[2e^(4x)cos(e(^4x))] / [sqrt sin(e^(4x)]
Explanation:
Applying chain rule
df(u)/dx= df/du .du/dx
let sin e^(4x) =u
d/du √u . d/dx (sin(e^(4x)))
we have,
d/du √u=1/(2√u)
and
d/dx (sin(e^(4x)))
Applying chain rule,
df(u)/dx= df/du .du/dx
let
Applying chain rule,
df(u)/dx= df/du .du/dx
let 4x=u
solving it we get,
now, cos(u)
u=
= cos(
Finally,
Substitute u= sin(
=
simplifying we get,