Solve m^-6/m^5

$$\frac { m ^ { - 6 } } { m ^ { 5 } }$$

Differentiate w.r.t. m

$$-\frac{11}{m^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1}m^{-6-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{-11})$$

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}.

$$-11m^{-11-1}$$

Do the arithmetic.

$$-11m^{-12}$$

Evaluate

$$\frac{1}{m^{11}}$$

Solution Steps

Rewrite m^{5} as m^{-6}m^{11}. Cancel out m^{-6} in both numerator and denominator.

$$\frac{1}{m^{11}}$$