Solve -5/x^3*-x^5/3*-4/x*20/x^3

$$\frac { - 5 } { x ^ { 3 } } \times \frac { - x ^ { 5 } } { 3 } \times \frac { - 4 } { x } \times \frac { 20 } { x ^ { 3 } }$$

Evaluate

$$-\frac{400}{3x^{2}}$$

Short Solution Steps

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

$$\frac{-5\left(-x^{5}\right)}{x^{3}\times 3}\times \frac{-4}{x}\times \frac{20}{x^{3}}$$

Multiply \frac{-5\left(-x^{5}\right)}{x^{3}\times 3} times \frac{-4}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-x^{5}\right)\left(-4\right)}{x^{3}\times 3x}\times \frac{20}{x^{3}}$$

Multiply \frac{-5\left(-x^{5}\right)\left(-4\right)}{x^{3}\times 3x} times \frac{20}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-x^{5}\right)\left(-4\right)\times 20}{x^{3}\times 3xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{-5\left(-x^{5}\right)\left(-4\right)\times 20}{x^{4}\times 3x^{3}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{-5\left(-x^{5}\right)\left(-4\right)\times 20}{x^{7}\times 3}$$

Multiply -5 and -4 to get 20.

$$\frac{20\left(-x^{5}\right)\times 20}{x^{7}\times 3}$$

Multiply 20 and 20 to get 400.

$$\frac{400\left(-x^{5}\right)}{x^{7}\times 3}$$

Factor the expressions that are not already factored.

$$\frac{-400x^{5}}{3x^{7}}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{-400}{3x^{2}}$$

Differentiate w.r.t. x

$$\frac{800}{3x^{3}}$$