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

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

Differentiate w.r.t. x

$$-\frac{3}{x^{\frac{5}{2}}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-\frac{3}{2}})$$

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}.

$$-\frac{3}{2}\times 2x^{-\frac{3}{2}-1}$$

Do the arithmetic.

$$-3x^{-\frac{5}{2}}$$

Evaluate

$$\frac{2}{x^{\frac{3}{2}}}$$