Solve Matrix

$$\frac { L L } { L } L \div \frac { G } { L } \tau$$

Evaluate

$$\frac{2\pi L^{3}}{G}$$

Solution Steps

Substitute 2 * \pi for \tau.

$$\frac{L L}{L} L / \frac{G}{L} 2 * \pi$$

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

$$\frac{\frac{L^{2}}{L}L}{\frac{G}{L}}\times 2\pi$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{L^{1}L}{\frac{G}{L}}\times 2\pi$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$\frac{L^{2}}{\frac{G}{L}}\times 2\pi$$

Divide L^{2} by \frac{G}{L} by multiplying L^{2} by the reciprocal of \frac{G}{L}.

$$\frac{L^{2}L}{G}\times 2\pi$$

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

$$\frac{L^{3}}{G}\times 2\pi$$

Express \frac{L^{3}}{G}\times 2 as a single fraction.

$$\frac{L^{3}\times 2}{G}\pi$$

Express \frac{L^{3}\times 2}{G}\pi as a single fraction.

$$\frac{L^{3}\times 2\pi }{G}$$

Differentiate w.r.t. L

$$\frac{6\pi L^{2}}{G}$$