Use logarithmic differentiation to find the derivative of the function y = x^{x + 9}. Use logarithmic differentiation to find the derivative of the function. { y = x^{2cosx}\ y'=... } Use logarithmic differentiation to find the derivative of the function y = (ln x)^{cos 4x}. Use...
Explain how to obtain the partial derivative of pressure with respect to volume at a constant temperature, using the 3 cases shown below. Ideal Gas Equation: An ideal gas is described by its three state variables {eq}P,T,V {/eq...
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The integral becomes:du/ (u^2 + 9)Next, 9 is factored out of the denominator:1/9 integeral du / ( (1/3u)^2 + 1)This is merely the derivative of the arctan function arctan(z) where z = 1/3uMaking this substitution z = 1/3u ---> dz = 1/3 du ---> 3 dz = duthe ...
If a graph of the first derivative is given, then a point of inflection occurs at x = a if at x = a the graph of f '(x) changes from either increasing to decreasing OR decreasing to increasing. Absolute Maximum or Absolute Minimum The candidates are the critical values of f (x) ...
Given \csc(x) = -\frac{5}{3} with (x) \in Q4 and \cos(y) = -\frac{\sqrt{2{3} with (y) \in Q2, find \sin(y - x). How do you prove cos^2(x) - sin^2(x) = 2cos^2(x) - 1? Prove that the derivative of csc x is -csc x cot x. ...
Find the derivative y=\sin ^{2}(\theta )+\theta \sin (\theta )+\cos ^{2}(\frac{\pi }{6})-\sqrt[3]{\theta } Recall that \frac{d}{dx}(\sec(x)) - \sec(x) \tan (x). Use the Quotient Rule and your knowledge of the derivative of sine and c...
Show how to find the Taylor series of (1+x)−1x centered at x=0. Taylor Series: The Taylor series is used to express the function as the infinite sum of the derivative terms at a point. If the derivative of a point is zero, the Taylor series is called a Macla...
(b) Find the derivative of the function f. (c) Find the domain of f'. (d) Determine the value(s) of x, if any, at which the function is not differentiable. (e) For what values of x does the gWhat is the derivative of a function? How is it...
How would you find y' if xy=yxusing logarithmic differentiation and keeping the answer in terms of x and y?Logarithmic Differentiation:The method of finding the derivative of a function by taking the logarithmic in both sides of the given equation and ...