So we are to derivate e^x^2
So we are using the rule (e^kx)'=k*e^kx
So we made e^x^2 to e^x*x since x^2 is the same as x*x
Which makes it xe^x^2
But the solution says its 2x*e^x^2
So we dont know why it's 2x and not just x, as we take the k from ^kx, which is x*x, so it should be just x?
So we are using the rule (e^kx)'=k*e^kx
So we made e^x^2 to e^x*x since x^2 is the same as x*x
Which makes it xe^x^2
But the solution says its 2x*e^x^2
So we dont know why it's 2x and not just x, as we take the k from ^kx, which is x*x, so it should be just x?
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e^x^2
for this use the chain rule: (dy/dx)(f(g(x))=f'(g(x))*(g'(x))
f(x) can be viewed as e^u (note: u=x^2)
g(x)x^2
f'=e^u
g'=2x
put it all together
e^x^2*(2x)
(2x)(e^x^2)
for this use the chain rule: (dy/dx)(f(g(x))=f'(g(x))*(g'(x))
f(x) can be viewed as e^u (note: u=x^2)
g(x)x^2
f'=e^u
g'=2x
put it all together
e^x^2*(2x)
(2x)(e^x^2)