Solve 2nm^6*4m^-1/2m^5n^6

$$\frac { 2 n m ^ { 6 } \cdot 4 m ^ { - 1 } } { 2 m ^ { 5 } n ^ { 6 } }$$

Evaluate

$$\frac{4}{n^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{2nm^{5}\times 4}{2m^{5}n^{6}}$$

Cancel out 2nm^{5} in both numerator and denominator.

$$\frac{4}{n^{5}}$$

Differentiate w.r.t. n

$$-\frac{20}{n^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{8m^{6}}{m\times 2m^{5}}n^{1-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n^{-5})$$

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}.

$$-5\times 4n^{-5-1}$$

Do the arithmetic.

$$-20n^{-6}$$