Solve x^0,5/x^-0,5

$$\frac { x ^ { 0,5 } } { x ^ { - 0,5 } }$$

Evaluate

$$x$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -0,5 from 0,5 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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{0,5-\left(-0,5\right)})$$

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.

$$1$$