** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** 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.

$\frac{d}{dx}\left(e^x-e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$

Learn how to solve differential calculus problems step by step online. Find the derivative of tan(e^x-e^(-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 a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function. Applying the derivative of the exponential function.

** Final Answer

**