Solve frac{-sqrt{45}y^2}{3sqrt{5}y}

$$\frac { - \sqrt { 45 } y ^ { 2 } } { 3 \sqrt { 5 } y }$$

Evaluate

$$-y$$

Short Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{\left(-\sqrt{45}\right)y}{3\sqrt{5}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\left(-3\sqrt{5}\right)y}{3\sqrt{5}}$$

Factor the expressions that are not already factored.

$$\frac{-3\sqrt{5}y}{3\sqrt{5}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\sqrt{5}y}{\sqrt{5}}$$

Rationalize the denominator of \frac{-\sqrt{5}y}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-\sqrt{5}y\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-\sqrt{5}y\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{-5y}{5}$$

Cancel out 5 and 5.

$$-y$$

Differentiate w.r.t. y

$$-1$$

Steps Using Definition of a Derivative

Cancel out y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\left(-\sqrt{45}\right)y}{3\sqrt{5}})$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\left(-3\sqrt{5}\right)y}{3\sqrt{5}})$$

Factor the expressions that are not already factored in \frac{\left(-3\sqrt{5}\right)y}{3\sqrt{5}}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-3\sqrt{5}y}{3\sqrt{5}})$$

Cancel out 3 in both numerator and denominator.

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

Rationalize the denominator of \frac{-\sqrt{5}y}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Cancel out 5 and 5.

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

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

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

Subtract 1 from 1.

$$-y^{0}$$

For any term t except 0, t^{0}=1.

$$-1$$