Solve -28k^2mn/-42km^3n=

$$\frac { - 28 k ^ { 2 } m n } { - 42 k m ^ { 3 } n } =$$

Differentiate w.r.t. k

$$\frac{2}{3m^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\left(-\frac{28mn}{-42nm^{3}}\right)k^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{2}{3m^{2}}k^{1})$$

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}.

$$\frac{2}{3m^{2}}k^{1-1}$$

Do the arithmetic.

$$\frac{2}{3m^{2}}k^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{2}{3m^{2}}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{3m^{2}}$$

Evaluate

$$\frac{2k}{3m^{2}}$$

Solution Steps

Cancel out 14kmn in both numerator and denominator.

$$\frac{-2k}{-3m^{2}}$$