Question

differentiation y=ex dx/dy
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Answer 1

Answer:

In implicit differentiation, we differentiate each side of an equation with two variables (usually xxx and yyy) by treating one of the variables as a function of the other. This calls for using the chain rule.

Let's differentiate x^2+y^2=1x2+y2=1x, squared, plus, y, squared, equals, 1 for example. Here, we treat yyy as an implicit function of xxx.

\begin{aligned} x^2+y^2&=1 \\\\ \dfrac{d}{dx}(x^2+y^2)&=\dfrac{d}{dx}(1) \\\\ \dfrac{d}{dx}(x^2)+\dfrac{d}{dx}(y^2)&=0 \\\\ 2x+2y\cdot\dfrac{dy}{dx}&=0 \\\\ 2y\cdot\dfrac{dy}{dx}&=-2x \\\\ \dfrac{dy}{dx}&=-\dfrac{x}{y} \end{aligned}x2+y2dxd(x2+y2)dxd(x2)+dxd(y2)2x+2y⋅dxdy2y⋅dxdydxdy=1=dxd(1)=0=0=−2x=−yx