Solve 6x/10*6x/3x^3

$$\frac { 6 x } { 10 } \cdot \frac { 6 x } { 3 x ^ { 3 } }$$

Evaluate

$$\frac{6}{5x}$$

Solution Steps

Divide 6x by 10 to get \frac{3}{5}x.

$$\frac{3}{5}x\times \frac{6x}{3x^{3}}$$

Cancel out 3x in both numerator and denominator.

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

Multiply \frac{3}{5} times \frac{2}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 2 to get 6.

$$\frac{6}{5x^{2}}x$$

Express \frac{6}{5x^{2}}x as a single fraction.

$$\frac{6x}{5x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{6}{5x}$$

Differentiate w.r.t. x

$$-\frac{6}{5x^{2}}$$