Solve frac{a^-1a^frac{3{8}}}{5}

$$\frac { a ^ { - 1 } a ^ { \frac { 3 } { 8 } } } { 5 }$$

Differentiate w.r.t. a

$$-\frac{1}{8a^{\frac{13}{8}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -1 and \frac{3}{8} to get -\frac{5}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-\frac{5}{8}}}{5})$$

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

$$-\frac{5}{8}\times \frac{1}{5}a^{-\frac{5}{8}-1}$$

Multiply -\frac{5}{8} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{1}{8}a^{-\frac{5}{8}-1}$$

Subtract 1 from -\frac{5}{8}.

$$-\frac{1}{8}a^{-\frac{13}{8}}$$

Evaluate

$$\frac{1}{5a^{\frac{5}{8}}}$$