Solve (2y)^-1

$$( 2 y ) ^ { - 1 }$$

Evaluate

$$\frac{1}{2y}$$

Solution Steps

Expand \left(2y\right)^{-1}.

$$2^{-1}y^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{1}{2}y^{-1}$$

Differentiate w.r.t. y

$$-\frac{1}{2y^{2}}$$

Steps Using Definition of a Derivative

Expand \left(2y\right)^{-1}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2^{-1}y^{-1})$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{2}y^{-1})$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{1}{2}y^{-1-1}$$

Subtract 1 from -1.

$$-\frac{1}{2}y^{-2}$$