Solve (x^3y^-2)*(x^-3y^5)

$$( x ^ { 3 } y ^ { - 2 } ) \times ( x ^ { - 3 } y ^ { 5 } )$$

Evaluate

$$y^{3}$$

Solution Steps

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

$$y^{-2}y^{5}$$

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$y^{3}$$

Differentiate w.r.t. y

$$3y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-2}y^{5})$$

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3})$$

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

$$3y^{3-1}$$

Subtract 1 from 3.

$$3y^{2}$$