Solve frac{b^-frac{3{2}}}{5/2}

$$\frac { b ^ { - \frac { 3 } { 2 } } } { \frac { 5 } { 2 } }$$

Differentiate w.r.t. b

$$-\frac{3}{5b^{\frac{5}{2}}}$$

Steps Using Definition of a Derivative

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

$$-\frac{3}{2}\times \frac{2}{5}b^{-\frac{3}{2}-1}$$

Multiply -\frac{3}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{3}{5}b^{-\frac{3}{2}-1}$$

Subtract 1 from -\frac{3}{2}.

$$-\frac{3}{5}b^{-\frac{5}{2}}$$

Evaluate

$$\frac{2}{5b^{\frac{3}{2}}}$$

Solution Steps

Divide b^{-\frac{3}{2}} by \frac{5}{2} by multiplying b^{-\frac{3}{2}} by the reciprocal of \frac{5}{2}.

$$\frac{b^{-\frac{3}{2}}\times 2}{5}$$