Solve -14mn^2k/4m^2n

$$\frac { - 14 m n ^ { 2 } k } { 4 m ^ { 2 } n }$$

Differentiate w.r.t. m

$$\frac{7kn}{2m^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-\frac{14kn^{2}}{4n}\right)m^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-\frac{7kn}{2}\right)\times \frac{1}{m})$$

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}.

$$-\left(-\frac{7kn}{2}\right)m^{-1-1}$$

Do the arithmetic.

$$\frac{7kn}{2}m^{-2}$$

Evaluate

$$-\frac{7kn}{2m}$$

Solution Steps

Cancel out 2mn in both numerator and denominator.

$$\frac{-7kn}{2m}$$