Question
In Exercises 13 through 24 , find the indicated partial derivatives by holding all but one of the variables constant and applying theorems for ordinary differentiation.$$f(x, y)=\frac{x+y}{\sqrt{y^{2}-x^{2}}} ; D_{2} f(x, y)$$
Step 1
To do this, we treat x as a constant and differentiate f(x, y) with respect to y. f(x, y) = (x + y) / √(y² - x²) Now, let's use the quotient rule for differentiation: (d/dy) [u(y) / v(y)] = (v(y) * (d/dy)u(y) - u(y) * (d/dy)v(y)) / [v(y)]² Here, u(y) = x + y Show more…
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In Exercises $13-24,$ find the derivative of $y$ with respect to the appropriate variable. $$ \begin{array}{l}{y=\left(x^{2}+1\right) \operatorname{sech}(\ln x)} \\ {\text { (Hint: Before differentiating, express in terms of exponentials and simplify.) }}\end{array} $$
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In Exercises $13-24,$ find the derivative of $y$ with respect to the appropriate variable. $y=\left(x^{2}+1\right) \operatorname{sech}(\ln x)$ (Hint: Before differentiating, express in terms of exponentials and simplify.)
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