Solve frac{x^frac{1{2}}}{x^-frac{1{2}}}

$$\frac { x ^ { \frac { 1 } { 2 } } } { x ^ { - \frac { 1 } { 2 } } }$$

Evaluate

$$x$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{1}{2} from \frac{1}{2} to get 1.

$$x^{1}$$

Calculate x to the power of 1 and get x.

$$x$$

Differentiate w.r.t. x

$$1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Do the arithmetic.

$$x^{0}$$

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

$$1$$