Write the trigonometric expression as an algebraic expression in $u$. \[ \tan \left(\sin ^{-1} \mathrm{u}\right) \] $\tan \left(\sin ^{-1} u\right)=\square($ Type an exact answer, using radicals as needed. $)$

Step 1 ：The given expression is a composition of trigonometric functions. We have the tangent of arcsine of u.

Step 2 ：To convert this into an algebraic expression, we can use the Pythagorean identity and the definition of tangent.

Step 3 ：The Pythagorean identity is \(sin^2(x) + cos^2(x) = 1\). Since we have arcsine of u, we can consider u as the sine of the angle.

Step 4 ：Therefore, we can express cosine of the angle in terms of u using the Pythagorean identity. The cosine is \(\sqrt{1 - u^2}\).

Step 5 ：The definition of tangent is \(tan(x) = sin(x)/cos(x)\). We can substitute the expressions of sine and cosine in terms of u into this definition to get the algebraic expression of the given trigonometric expression.

Step 6 ：Substituting, we get \(tan(x) = \frac{u}{\sqrt{1 - u^2}}\).

Step 7 ：Final Answer: The algebraic expression of the given trigonometric expression is \(\boxed{\frac{u}{\sqrt{1 - u^2}}}\).