Solve 3/7x^{5}x^{8}z^8:(-1/14x^5y^6z^6)=

$$\frac { 3 } { 7 } x ^ { 5 } x ^ { 8 } z ^ { 8 } : ( - \frac { 1 } { 14 } x ^ { 5 } y ^ { 6 } z ^ { 6 } ) =$$

Evaluate

$$-\frac{6z^{2}x^{8}}{y^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$\frac{\frac{3}{7}x^{13}z^{8}}{-\frac{1}{14}x^{5}y^{6}z^{6}}$$

Cancel out x^{5}z^{6} in both numerator and denominator.

$$\frac{\frac{3}{7}z^{2}x^{8}}{-\frac{1}{14}y^{6}}$$

Differentiate w.r.t. x

$$-\frac{48z^{2}x^{7}}{y^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{8}z^{8}}{7\left(-\frac{y^{6}z^{6}}{14}\right)}x^{5-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{6z^{2}x^{8}}{y^{6}}\right)x^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{6z^{2}x^{8}}{y^{6}})$$

The derivative of a constant term is 0.

$$0$$