How do you find the derivative of y=sin x^2?

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Answer 1 · 2018-05-18T13:39:59

#2xcos(x^2)#

Given: #y=sin(x^2)#.

Use the chain rule, which states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=x^2,:.(du)/dx=2x#.

Then, #y=sinu,:.dy/(du)=cosu#.

And so,

#dy/dx=cosu*2x#

#=2xcosu#

Substituting back #u=x^2#, we get:

#=2xcos(x^2)#