Solve frac{16m^{36}n^{28}p^18}{4m^18n^14p^9}

$$\frac { 16 m ^ { 36 } n ^ { 28 } p ^ { 18 } } { 4 m ^ { 18 } n ^ { 14 } p ^ { 9 } }$$

Differentiate w.r.t. m

$$72p^{9}n^{14}m^{17}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{16p^{18}n^{28}}{4p^{9}n^{14}}m^{36-18})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4p^{9}n^{14}m^{18})$$

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}.

$$18\times 4p^{9}n^{14}m^{18-1}$$

Do the arithmetic.

$$72p^{9}n^{14}m^{17}$$

Evaluate

$$4p^{9}n^{14}m^{18}$$

Solution Steps

Cancel out 4p^{9}n^{14}m^{18} in both numerator and denominator.

$$4p^{9}n^{14}m^{18}$$