Solve 1/3pi*x^2*5x/x-5

$$\frac{ 1 }{ 3 } \pi \times { x }^{ 2 } \times \frac{ 5x }{ x-5 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{1}{3} times \frac{5x}{x-5} by multiplying numerator times numerator and denominator times denominator.

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

Use the distributive property to multiply 3 by x-5.

$$\frac{5x}{3x-15}\pi x^{2}$$

Express \frac{5x}{3x-15}\pi as a single fraction.

$$\frac{5x\pi }{3x-15}x^{2}$$

Express \frac{5x\pi }{3x-15}x^{2} as a single fraction.

$$\frac{5x\pi x^{2}}{3x-15}$$

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

$$\frac{5x^{3}\pi }{3x-15}$$

Differentiate w.r.t. x

$$\frac{5\pi \times \left(\frac{x}{x-5}\right)^{2}\left(2x-15\right)}{3}$$