Solve frac{frac{xsqrt{x}}{3}a}{frac{3sqrt{x}}{x}}

$$\frac { \frac { x \sqrt { x } } { 3 } a } { \frac { 3 \sqrt { x } } { x } }$$

Evaluate

$$\frac{ax^{2}}{9}$$

Short Solution Steps

Express \frac{x\sqrt{x}}{3}a as a single fraction.

$$\frac{\frac{x\sqrt{x}a}{3}}{\frac{3\sqrt{x}}{x}}$$

Cancel out \sqrt{x} in both numerator and denominator.

$$\frac{\frac{x\sqrt{x}a}{3}}{\frac{3}{\sqrt{x}}}$$

Divide \frac{x\sqrt{x}a}{3} by \frac{3}{\sqrt{x}} by multiplying \frac{x\sqrt{x}a}{3} by the reciprocal of \frac{3}{\sqrt{x}}.

$$\frac{x\sqrt{x}a\sqrt{x}}{3\times 3}$$

Multiply \sqrt{x} and \sqrt{x} to get \left(\sqrt{x}\right)^{2}.

$$\frac{x\left(\sqrt{x}\right)^{2}a}{3\times 3}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$\frac{xxa}{3\times 3}$$

Multiply x and x to get x^{2}.

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

Multiply 3 and 3 to get 9.

$$\frac{x^{2}a}{9}$$

Differentiate w.r.t. x

$$\frac{2ax}{9}$$