Find the dy/dx of the equation y=e^-x^2
equations do not have derivatives; functions do.
for tis, use the chain rule: (e^u)' = e^u u'
y = e^(-x^2)
y' = e^(-x^2) (-2x) = -2x e^(-x^2)
To find the derivative dy/dx of the equation y = e^(-x^2), we can use the chain rule of differentiation.
First, we differentiate the outer function, which in this case is e^(-x^2). The derivative of e^u with respect to u is simply e^u. So, differentiating e^(-x^2) with respect to x gives us e^(-x^2).
Next, we need to differentiate the inner function -x^2. The derivative of -x^2 with respect to x is -2x.
Finally, we apply the chain rule by multiplying the derivative of the outer function (e^(-x^2)) with respect to x, which is e^(-x^2), by the derivative of the inner function (-2x).
Therefore, dy/dx = e^(-x^2) * (-2x), which simplifies to -2xe^(-x^2).