Derivative of 1y\frac{1}{y}

The calculator will find the derivative of 1y\frac{1}{y}, with steps shown.

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Your Input

Find ddy(1y)\frac{d}{dy} \left(\frac{1}{y}\right).

Solution

Apply the power rule ddy(yn)=nyn1\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1} with n=1n = -1:

(ddy(1y))=(1y2){\color{red}\left(\frac{d}{dy} \left(\frac{1}{y}\right)\right)} = {\color{red}\left(- \frac{1}{y^{2}}\right)}

Thus, ddy(1y)=1y2\frac{d}{dy} \left(\frac{1}{y}\right) = - \frac{1}{y^{2}}.

Answer

ddy(1y)=1y2\frac{d}{dy} \left(\frac{1}{y}\right) = - \frac{1}{y^{2}}A