(The value of \(B′(0)\) for an arbitrary function of the form \(B(x)=b^x, \,b>0,\) will be derived later. Just be aware that not all of the forms below are mathematically correct. We were introduced to hyperbolic functions in Introduction to Functions and Graphs, along with some of their basic properties. Finally, just a note on syntax and notation: the exponential function ex2 is sometimes written in the forms shown below (the derivative of each is as per the calculations above). 6.9.3 Describe the common applied conditions of a catenary curve. We see that on the basis of the assumption that \(B(x)=b^x\) is differentiable at \(0,B(x)\) is not only differentiable everywhere, but its derivative isįor \(E(x)=e^x, \,E′(0)=1.\) Thus, we have \(E′(x)=e^x\). 6.9.2 Apply the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals.
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