Solve (64u)^-frac{3{2}}

$$( 64 u ) ^ { - \frac { 3 } { 2 } }$$

Evaluate

$$\frac{1}{512u^{\frac{3}{2}}}$$

Solution Steps

Expand \left(64u\right)^{-\frac{3}{2}}.

$$64^{-\frac{3}{2}}u^{-\frac{3}{2}}$$

Calculate 64 to the power of -\frac{3}{2} and get \frac{1}{512}.

$$\frac{1}{512}u^{-\frac{3}{2}}$$

Differentiate w.r.t. u

$$-\frac{3}{1024u^{\frac{5}{2}}}$$

Steps Using Definition of a Derivative

Expand \left(64u\right)^{-\frac{3}{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(64^{-\frac{3}{2}}u^{-\frac{3}{2}})$$

Calculate 64 to the power of -\frac{3}{2} and get \frac{1}{512}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{512}u^{-\frac{3}{2}})$$

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

$$-\frac{3}{2}\times \frac{1}{512}u^{-\frac{3}{2}-1}$$

Multiply -\frac{3}{2} times \frac{1}{512} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{3}{1024}u^{-\frac{3}{2}-1}$$

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

$$-\frac{3}{1024}u^{-\frac{5}{2}}$$