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

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

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

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

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

Multiply \frac{1}{2} times -2.

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

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

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

Evaluate

$$-2\sqrt{x}$$

Solution Steps

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

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