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

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

Differentiate w.r.t. x

$$-\frac{1}{4\sqrt{x}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -\frac{1}{2} and 1 to get \frac{1}{2}.

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

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

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

Multiply \frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{1}{4}x^{\frac{1}{2}-1}$$

Subtract 1 from \frac{1}{2}.

$$-\frac{1}{4}x^{-\frac{1}{2}}$$

Evaluate

$$-\frac{\sqrt{x}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -\frac{1}{2} and 1 to get \frac{1}{2}.

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