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How do you differentiate #y=e^(x^2)#?

1 Answer
Sep 17, 2016

Answer:

#(dy)/(dx)=2xe^(x^2)#

Explanation:

Chain Rule - In order to differentiate a function of a function, say #y, =f(g(x))#, where we have to find #(dy)/(dx)#, we need to do (a) substitute #u=g(x)#, which gives us #y=f(u)#. Then we need to use a formula called Chain Rule, which states that #(dy)/(dx)=(dy)/(du)xx(du)/(dx)#. In fact if we have something like #y=f(g(h(x)))#, we can have #(dy)/(dx)=(dy)/(df)xx(df)/(dg)xx(dg)/(dh)#

Here we have #y=e^u#, where #u=x^2#

Hence, #(dy)/(dx)=(dy)/(du)xx(du)/(dx)#

= #d/(du)e^uxxd/dx(x^2)#

= #e^uxx2x=2xe^(x^2)#