Solve x^3y^2divx^3y

$$x ^ { 3 } y ^ { 2 } \div x ^ { 3 } y$$

Evaluate

$$y^{3}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$y^{2}y$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y^{3}$$

Differentiate w.r.t. y

$$3y^{2}$$

Steps Using Definition of a Derivative

Cancel out x^{3} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 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.

$$3y^{2}$$