Solve 1/a:(-1/a)^2

$$\frac { 1 } { a } : ( - \frac { 1 } { a } ) ^ { 2 }$$

Evaluate

$$a$$

Solution Steps

Calculate -\frac{1}{a} to the power of 2 and get \left(\frac{1}{a}\right)^{2}.

$$\frac{\frac{1}{a}}{\left(\frac{1}{a}\right)^{2}}$$

To raise \frac{1}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{1}{a}}{\frac{1^{2}}{a^{2}}}$$

Divide \frac{1}{a} by \frac{1^{2}}{a^{2}} by multiplying \frac{1}{a} by the reciprocal of \frac{1^{2}}{a^{2}}.

$$\frac{a^{2}}{a\times 1^{2}}$$

Cancel out a in both numerator and denominator.

$$\frac{a}{1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{a}{1}$$

Anything divided by one gives itself.

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

Calculate -\frac{1}{a} to the power of 2 and get \left(\frac{1}{a}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a}}{\left(\frac{1}{a}\right)^{2}})$$

To raise \frac{1}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a}}{\frac{1^{2}}{a^{2}}})$$

Divide \frac{1}{a} by \frac{1^{2}}{a^{2}} by multiplying \frac{1}{a} by the reciprocal of \frac{1^{2}}{a^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{a\times 1^{2}})$$

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{1^{2}})$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

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

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

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

$$1$$