Solve -12m^-19n^10/-76m^18n^3

$$\frac { - 12 m ^ { - 19 } n ^ { 10 } } { - 76 m ^ { 18 } n ^ { 3 } }$$

Evaluate

$$\frac{3n^{7}}{19m^{37}}$$

Solution Steps

Cancel out 4n^{3} in both numerator and denominator.

$$\frac{-3m^{-19}n^{7}}{-19m^{18}}$$

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

$$\frac{-3n^{7}}{-19m^{37}}$$

Differentiate w.r.t. m

$$-\frac{111n^{7}}{19m^{38}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-\frac{12n^{10}}{-76n^{3}}\right)m^{-19-18})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3n^{7}}{19}m^{-37})$$

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}.

$$-37\times \frac{3n^{7}}{19}m^{-37-1}$$

Do the arithmetic.

$$\left(-\frac{111n^{7}}{19}\right)m^{-38}$$