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) ...
Prove that the derivative of csc(x) is -csc(x)cot(x) (i.e. f(x) = csc(x) \to f'(x) = -csc(x)cot(x)). If F(x) = cot(x) , prove F'(x) = -csc^2(x) . Prove the following identity. cosx/1-sinx - cosx/1+sinx = 2tanx ...
use the limit definition of derivative to explain why \frac{\mathrm{d} }{\mathrm{d} x}[ cos(x)] = - sin (x). hint: you will need to use the fact that \lim_{h \rightarrow 0} \frac{cos ( h) - 1}{ h} = find the limit. lim x->pi/2 cosx/1-sinx. With explanation?
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...
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 ...