Exponential and Logarithmic Functions & Inverse Derivative-Questions and Answers Graded A+

Exponential and Logarithmic Functions & Inverse Derivative-Questions and Answers Graded A+ If y=lnx, then y'= - ANSWER-1/x If y=lnu, then y'= - ANSWER-u'/u If y=eˣ, then y'= - ANSWER-eˣ If y=eᵘ, then y'= - ANSWER-u'×eᵘ If y=loga(x), then y'= - ANSWER-1/(xlna) If y=loga(u), then y'= - ANSWER-u'/(ulna) If y=aˣ, then y'= - ANSWER-aˣ(lna) If y=aᵘ, then y'= - ANSWER-aᵘ×u'×lna ln1 - ANSWER-0 e⁰ - ANSWER-1 lne - ANSWER-1 lneˣ - ANSWER-x Inverse Derivative Steps - ANSWER-1 Find f'(x) 2 Set f(x) to a & solve for x, x=b 3 Find f'(b) 4 The (f^-1)'(a)=1/f'(b) Let f be a function that is differentiable on an interval I. If f has an inverse function then the following statements are true: - ANSWER-1. If f is continuous on its domain, then f⁻¹ is continuous on its domain 2. If f is increasing on its domain, then f⁻¹ is increasing on its domain. 3. If f is decreasing on its domain, then f⁻¹ is decreasing on its domain. 4. If f is differentiable at c and f'(c)≠0, then f⁻¹ is differentiable at f(c). Steps to show that the slopes of the graphs f(x) and f^-1(x) at (a,b) and (b,a) are recirpocals - ANSWER-1 Find the derivatives of both 2 Plug in the x-component of each of the corresponding points into the derivatives