Concept explainers
Logarithmic differentiation Use logarithmic differentiation to evaluate f′(x).
64.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus and Its Applications (11th Edition)
- Differential calculus y = f (x) count to the sixth derivativearrow_forwardDerivatives by different methods Calculate the derivative of the following functions (i) using the fact that bx = ex ln b and (ii) using logarithmic differentiation. Verify that both answers are the same. y =1x2 + 12xarrow_forwardQuotient Rule for the second derivative Assuming the firstand second derivatives of f and g exist at x, find a formula ford2/dx 2 (f(x)/g(x))arrow_forward
- Using trignometric finction/s:- Find the derivative of the function g(x) = sin2 x + cos2 +x in two ways.arrow_forwardProduct Rule for the second derivative Assuming the firstand second derivatives of f and g exist at x, find a formula ford2/dx 2 (f(x)g(x)).arrow_forwardShow your work. Use DEFINITION to find the derivatives of the following functions. Do not use the formulas. 1. f(x) = tan x 2. f(x) = x3 3. f(x) = x2arrow_forward
- Elimination of Arbitrary Constants by Differentiation & Combination.arrow_forwardUsing Leibniz find the third derivative of the following function y=x2cos3x Find the local linear approximation L(x) of the function f(x)=lnx at x=1 .arrow_forwardUsing differentiation, integration, s-shifting, or convolution, and showing the details: find f(t) if L(f) equalsarrow_forward
- The definition of the derivative function is f′(x)=f(x+h)−f(x)h.f′(x)=h→0limhf(x+h)−f(x). Use this definition to calculate the derivative of f(x)=3x+1f(x)=3x+1. Show all work.arrow_forward10- f(x) defined and continuous in the range [0,7] and inverse derivative of f(x) is F(x). what is F(7) for the given equals?arrow_forwardconsider the following about a function f(x). the derivation f(x) is positive from(-1,0) and (1,\infty ), and the derivative f^'(x) is negative from (-\infty ,-1)and (0,1) What does f(x) resemble?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage