Final answer to the problem
$\mathrm{csch}\left(\frac{x}{7}\right)+\frac{-x\mathrm{cosh}\left(\frac{x}{7}\right)}{7\mathrm{sinh}\left(\frac{x}{7}\right)^{2}}+\frac{x}{\sqrt{49-x^2}}$
Got another answer? Verify it here!
Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(xsinh(x/7)^(-1)-(49-x^2)^(1/2)) using the sum rule. 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 is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\mathrm{sinh}\left(\frac{x}{7}\right)^{-1}. The derivative of the linear function is equal to 1.
Final answer to the problem
$\mathrm{csch}\left(\frac{x}{7}\right)+\frac{-x\mathrm{cosh}\left(\frac{x}{7}\right)}{7\mathrm{sinh}\left(\frac{x}{7}\right)^{2}}+\frac{x}{\sqrt{49-x^2}}$
