Solve dx*(dx)^frac{1{2}}

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

Evaluate

$$dx\sqrt{dx}$$

Solution Steps

Expand \left(dx\right)^{\frac{1}{2}}.

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

To multiply powers of the same base, add their exponents. Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$d^{\frac{3}{2}}xx^{\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

Differentiate w.r.t. x

$$\frac{2|\frac{x}{d}|d+x}{2\sqrt{\frac{x}{d^{3}}}}$$