Solve frac{4m^-frac{1{3}}}{m^frac{4{3}}}=

$$\frac { 4 m ^ { - \frac { 1 } { 3 } } } { m ^ { \frac { 4 } { 3 } } } =$$

Differentiate w.r.t. m

$$-\frac{20}{3m^{\frac{8}{3}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{1}m^{-\frac{1}{3}-\frac{4}{3}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m^{-\frac{5}{3}})$$

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}.

$$-\frac{5}{3}\times 4m^{-\frac{5}{3}-1}$$

Do the arithmetic.

$$-\frac{20}{3}m^{-\frac{8}{3}}$$

Evaluate

$$\frac{4}{m^{\frac{5}{3}}}$$