Solve 5y^3/x^2*x^2/y

$$\frac { 5 y ^ { 3 } } { x ^ { 2 } } \times \frac { x ^ { 2 } } { y }$$

Evaluate

$$5y^{2}$$

Solution Steps

Multiply \frac{5y^{3}}{x^{2}} times \frac{x^{2}}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5y^{3}x^{2}}{x^{2}y}$$

Cancel out yx^{2} in both numerator and denominator.

$$5y^{2}$$

Differentiate w.r.t. y

$$10y$$

Steps Using Definition of a Derivative

Multiply \frac{5y^{3}}{x^{2}} times \frac{x^{2}}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5y^{3}x^{2}}{x^{2}y})$$

Cancel out yx^{2} in both numerator and denominator.

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

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

$$2\times 5y^{2-1}$$

Multiply 2 times 5.

$$10y^{2-1}$$

Subtract 1 from 2.

$$10y^{1}$$

For any term t, t^{1}=t.

$$10y$$