Derivative of y = e^(x^2)

In this article we will be teaching you how to find the derivative of this function using the chain rule. After finding the result we’ll tell you quick and short methods on how to easily get the derivative of any e function. So, let's begin with the chain rule: y equals to e to the x squared, and we’ve also got u equals to x squared. So from the chain rule we know that dy dx equals to dy du times du dx. So on our left hand side we basically have the same as y equals to e to the u because we have u equals to x squared here. So one more thing you need to know about exponentials is that the derivative of e to the x is just e to the x. So if we apply this here, we have dy du equals to e to the u. So now we found dy du, and our next job is to find du dx. So du dx equals to 2x. So now we have everything and we just plug into our formula over here. Dy du equals to e to the u times du dx which is 2x. Our last step is to replace the u with x squared because we want everything in terms of x. So we have e to the x squared times 2x, and that is our answer to the derivative. So, hopefully you can see in this result that the easiest way to find the derivative of any e function with the chain rule is to just find the derivative of the index and in this case our index is x squared.


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