Solve s^-frac{17{6}}div(s^-frac{7{6}}divs^-frac{6{7}})

$$s ^ { - \frac { 17 } { 6 } } \div ( s ^ { - \frac { 7 } { 6 } } \div s ^ { - \frac { 6 } { 7 } } )$$

Differentiate w.r.t. s

$$-\frac{53}{21s^{\frac{74}{21}}}$$

Steps Using Definition of a Derivative

Rewrite s^{-\frac{6}{7}} as s^{-\frac{7}{6}}s^{\frac{13}{42}}. Cancel out s^{-\frac{7}{6}} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{s^{-\frac{17}{6}}}{\frac{1}{s^{\frac{13}{42}}}})$$

Divide s^{-\frac{17}{6}} by \frac{1}{s^{\frac{13}{42}}} by multiplying s^{-\frac{17}{6}} by the reciprocal of \frac{1}{s^{\frac{13}{42}}}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{-\frac{17}{6}}s^{\frac{13}{42}})$$

To multiply powers of the same base, add their exponents. Add -\frac{17}{6} and \frac{13}{42} to get -\frac{53}{21}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{-\frac{53}{21}})$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{53}{21}s^{-\frac{53}{21}-1}$$

Subtract 1 from -\frac{53}{21}.

$$-\frac{53}{21}s^{-\frac{74}{21}}$$

Evaluate

$$\frac{1}{s^{\frac{53}{21}}}$$