Final Answer
Step-by-step Solution
Specify the solving method
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 ${f'(x) = sec^2(x)\cdot D_x(x)}$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\ln\left(x\right)\right)\sec\left(\ln\left(x\right)\right)^2$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(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 and term.