Solve -y-1/sqrt{7+0y}9/2

$$\frac { - y - 1 } { \sqrt { 7 + 0 y } } \frac { 9 } { 2 }$$

Evaluate

$$-\frac{9\sqrt{7}\left(y+1\right)}{14}$$

Solution Steps

Anything times zero gives zero.

$$\frac{-y-1}{\sqrt{7+0}}\times \frac{9}{2}$$

Add 7 and 0 to get 7.

$$\frac{-y-1}{\sqrt{7}}\times \frac{9}{2}$$

Rationalize the denominator of \frac{-y-1}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\left(-y-1\right)\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\times \frac{9}{2}$$

The square of \sqrt{7} is 7.

$$\frac{\left(-y-1\right)\sqrt{7}}{7}\times \frac{9}{2}$$

Multiply \frac{\left(-y-1\right)\sqrt{7}}{7} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-y-1\right)\sqrt{7}\times 9}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{\left(-y-1\right)\sqrt{7}\times 9}{14}$$

Use the distributive property to multiply -y-1 by \sqrt{7}.

$$\frac{\left(-y\sqrt{7}-\sqrt{7}\right)\times 9}{14}$$

Use the distributive property to multiply -y\sqrt{7}-\sqrt{7} by 9.

$$\frac{-9y\sqrt{7}-9\sqrt{7}}{14}$$

Differentiate w.r.t. y

$$-\frac{9 \sqrt{7}}{14} = -1.7008401285415224$$