Solve (49s)^-frac{1{2}}

$$( 49 s ) ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{1}{7\sqrt{s}}$$

Solution Steps

Expand \left(49s\right)^{-\frac{1}{2}}.

$$49^{-\frac{1}{2}}s^{-\frac{1}{2}}$$

Calculate 49 to the power of -\frac{1}{2} and get \frac{1}{7}.

$$\frac{1}{7}s^{-\frac{1}{2}}$$

Differentiate w.r.t. s

$$-\frac{1}{14s^{\frac{3}{2}}}$$

Steps Using Definition of a Derivative

Expand \left(49s\right)^{-\frac{1}{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(49^{-\frac{1}{2}}s^{-\frac{1}{2}})$$

Calculate 49 to the power of -\frac{1}{2} and get \frac{1}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{7}s^{-\frac{1}{2}})$$

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

$$-\frac{1}{2}\times \frac{1}{7}s^{-\frac{1}{2}-1}$$

Multiply -\frac{1}{2} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{1}{14}s^{-\frac{1}{2}-1}$$

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

$$-\frac{1}{14}s^{-\frac{3}{2}}$$