Solve A_{2}quad55frac{2sqrt{3}}{sqrt{3}+sqrt{3}}

$$A _ { 2 } \quad 55 \frac { 2 \sqrt { 3 } } { \sqrt { 3 } + \sqrt { 3 } }$$

Evaluate

$$55A_{2}$$

Solution Steps

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

$$55A_{2}\times \frac{2\sqrt{3}}{2\sqrt{3}}$$

Cancel out 2\sqrt{3} in both numerator and denominator.

$$55A_{2}\times 1$$

Multiply 55 and 1 to get 55.

$$55A_{2}$$

Differentiate w.r.t. A_2

$$55$$

Steps Using Definition of a Derivative

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

$$\frac{\mathrm{d}}{\mathrm{d}A_{2}}(55A_{2}\times \frac{2\sqrt{3}}{2\sqrt{3}})$$

Cancel out 2\sqrt{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}A_{2}}(55A_{2}\times 1)$$

Multiply 55 and 1 to get 55.

$$\frac{\mathrm{d}}{\mathrm{d}A_{2}}(55A_{2})$$

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

$$55A_{2}^{1-1}$$

Subtract 1 from 1.

$$55A_{2}^{0}$$

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

$$55\times 1$$

For any term t, t\times 1=t and 1t=t.

$$55$$