derivative of e (1 Viewer)

[Arithela]

diferentiate sin[e^(2x)]

help please

 

[foram]

diferentiate sin[e^(2x)]

help please

2e^2x .cos(e^2x) I think, using chain rule.

 

[Arithela]

thats right, show me working please

 

[pLuvia]

Let g(x) and f(y) be functions

d/dx(g(f(y)))=f'(y)g'([f(y)])
Hence
d/dx(sin[e^(2x)])
=2e^2x*cos[e^2x]

That's the only working you need

 

[foram]

y=sin(e^2x)
y'= dy/du . du/dx (chain rule)


let u=e^2x

dy/du = cos u
du/dx = 2e^2x
dy/du . du/dx = 2e^2x . cos(u)

= 2e^2x cos(e^2x)

 

[Mark576]

d/dx[sin(f(x))] = f'(x).cos(f(x)) and if f(x) = e^2x then f'(x) = 2e^2x
So then d/dx(sin(e^2x)) = 2e^2x.cos(e^2x)