Final answer to the problem
$\frac{-2\mathrm{sinh}\left(\frac{2x}{7}\right)}{7\mathrm{cosh}\left(\frac{2x}{7}\right)^{2}}$
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Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of cosh((2x)/7)^(-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 cosine. The derivative of a function multiplied by a constant (\frac{1}{7}) is equal to the constant times the derivative of the function. Multiply the fraction and term in - \left(\frac{1}{7}\right)\mathrm{cosh}\left(\frac{2x}{7}\right)^{-2}\frac{d}{dx}\left(2x\right)\mathrm{sinh}\left(\frac{2x}{7}\right).
Final answer to the problem
$\frac{-2\mathrm{sinh}\left(\frac{2x}{7}\right)}{7\mathrm{cosh}\left(\frac{2x}{7}\right)^{2}}$
