Solve 2a/3b^3*3b^2/4x*x^2/2a

$$\frac { 2 a } { 3 b ^ { 3 } } \times \frac { 3 b ^ { 2 } } { 4 x } \times \frac { x ^ { 2 } } { 2 a }$$

Evaluate

$$\frac{x}{4b}$$

Solution Steps

Multiply \frac{2a}{3b^{3}} times \frac{3b^{2}}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2a\times 3b^{2}}{3b^{3}\times 4x}\times \frac{x^{2}}{2a}$$

Cancel out 2\times 3b^{2} in both numerator and denominator.

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

Multiply \frac{a}{2bx} times \frac{x^{2}}{2a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ax^{2}}{2bx\times 2a}$$

Cancel out ax in both numerator and denominator.

$$\frac{x}{2\times 2b}$$

Multiply 2 and 2 to get 4.

$$\frac{x}{4b}$$

Differentiate w.r.t. x

$$\frac{1}{4b}$$