Solve (Delta)^-1(1/sqrt{14*sqrt{17}})

$$( \Delta ) ^ { - 1 } ( \frac { 1 } { \sqrt { 14 } \times \sqrt { 17 } } )$$

Evaluate

$$\frac{\sqrt{238}}{238\Delta }$$

Solution Steps

To multiply \sqrt{14} and \sqrt{17}, multiply the numbers under the square root.

$$\Delta ^{-1}\times \frac{1}{\sqrt{238}}$$

Rationalize the denominator of \frac{1}{\sqrt{238}} by multiplying numerator and denominator by \sqrt{238}.

$$\Delta ^{-1}\times \frac{\sqrt{238}}{\left(\sqrt{238}\right)^{2}}$$

The square of \sqrt{238} is 238.

$$\Delta ^{-1}\times \frac{\sqrt{238}}{238}$$

Express \Delta ^{-1}\times \frac{\sqrt{238}}{238} as a single fraction.

$$\frac{\Delta ^{-1}\sqrt{238}}{238}$$

Differentiate w.r.t. Δ

$$-\frac{\sqrt{238}}{238\Delta ^{2}}$$