Solve y^-1/y^3*y^-3

$$\frac { y ^ { - 1 } } { y ^ { 3 } \times y ^ { - 3 } }$$

Evaluate

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

Solution Steps

Multiply y^{3} and y^{-3} to get 1.

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

Anything divided by one gives itself.

$$y^{-1}$$

Differentiate w.r.t. y

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

Steps Using Definition of a Derivative

Multiply y^{3} and y^{-3} to get 1.

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

Anything divided by one gives itself.

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

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

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

Subtract 1 from -1.

$$-y^{-2}$$