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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 ${f'(x) = sec^2(x)\cdot D_x(x)}$
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$\frac{d}{dx}\left(e^x-e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$
Learn how to solve differential equations problems step by step online. Find the derivative using the product rule d/dx(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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-1 and g=e^{-x}. The derivative of the constant function (-1) is equal to zero.