Final answer to the problem
$\frac{\sec\left(\ln\left(x\right)\right)^2}{x}$
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Step-by-step Solution
Learn how to solve basic differentiation rules problems step by step online. Find the derivative of tan(ln(x)). The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Multiply the fraction by the term \sec\left(\ln\left(x\right)\right)^2. Any expression multiplied by 1 is equal to itself.
Final answer to the problem
$\frac{\sec\left(\ln\left(x\right)\right)^2}{x}$
