Solve 589x^5493x^3/5x^2

$$\frac { 589 x ^ { 5 } 493 x ^ { 3 } } { 5 x ^ { 2 } }$$

Evaluate

$$\frac{290377x^{6}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{589x^{8}\times 493}{5x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{493\times 589x^{6}}{5}$$

Multiply 493 and 589 to get 290377.

$$\frac{290377x^{6}}{5}$$

Differentiate w.r.t. x

$$\frac{1742262x^{5}}{5}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{290377x^{3}}{5}x^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{290377x^{3}}{5}x^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times \frac{290377x^{3}}{5}x^{3-1}$$

Do the arithmetic.

$$\frac{871131x^{3}}{5}x^{2}$$