Final answer to the problem
$\frac{-\mathrm{cosh}\left(\tan\left(x\right)\right)\sec\left(x\right)^2}{\mathrm{sinh}\left(\tan\left(x\right)\right)^{2}}$
Got another answer? Verify it here!
Step-by-step Solution
Learn how to solve power rule for derivatives problems step by step online. Find the derivative of sinh(tan(x))^(-1). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of hyperbolic sine. 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 linear function is equal to 1.
Final answer to the problem
$\frac{-\mathrm{cosh}\left(\tan\left(x\right)\right)\sec\left(x\right)^2}{\mathrm{sinh}\left(\tan\left(x\right)\right)^{2}}$
