Solve 2x/4bc^2*4a^2/4x^3=

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

Evaluate

$$\frac{\left(\frac{a}{cx}\right)^{2}}{2b}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

Cancel out 4 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Differentiate w.r.t. x

$$-\frac{\left(\frac{a}{c}\right)^{2}}{bx^{3}}$$