Solve pi/3*R^2*-5R/3-R

$$\frac { \pi } { 3 } \times R ^ { 2 } \times \frac { - 5 R } { 3 - R }$$

Evaluate

$$-\frac{5\pi R^{3}}{3\left(3-R\right)}$$

Short Solution Steps

Express \frac{\pi }{3}R^{2} as a single fraction.

$$\frac{\pi R^{2}}{3}\times \frac{-5R}{3-R}$$

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

$$\frac{\pi R^{2}\left(-5\right)R}{3\left(3-R\right)}$$

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

$$\frac{\pi R^{3}\left(-5\right)}{3\left(3-R\right)}$$

Use the distributive property to multiply 3 by 3-R.

$$\frac{\pi R^{3}\left(-5\right)}{9-3R}$$

Differentiate w.r.t. R

$$-\frac{5\pi \times \left(\frac{R}{R-3}\right)^{2}\left(9-2R\right)}{3}$$