3.3.1. Derivatives of Logarithmic FunctionsThe derivative of the logarithmic function is determined by thefollowing theorem.Theorem 3.3 Chain Rule of the Derivative of Logarithmic FunctionLet a be a positive real number (a # 1) and let u be a differentiablefunction of x and u(x) > 0, then1 duи dxdu(loga u)(In u)dx(In a)u dxdxThe second formula is a special case of the first formula since thenatural logarithm In u = log, u.In the first formula we can seta = e thus In a = In e = 1.Question:1. Find the derivative of the followingfunction:y = ln vtan x

Answered: Image /qna-images/answer/27fb65b1-7665-4027-b34f-f9ee7362aeef.jpg

Answered: estion: Find the derivative of the…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 57SE: Use a graphing utility to find an exponential regression formula f(x) and a logarithmic regression...

See similar textbooks

Similar questions

Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.
Use a graphing utility to find an exponential regression formula f(x) and a logarithmic regression formula g(x) for the points (1.5,1.5) and (8.5,8.5). Round all numbers to 6 decimal places. Graph the points and both formulas along with the line y=x on the same axis. Make a conjecture about the relationship of the regression formulas.
6-
Question 1. Using logarithmic differentiation, find the derivative of the given functions: a) x² – 5 f(x) = x > V5. || 1+ x7 b) g(x) = (In æ)", x > 1.
20-
3. (a) Use logarithmic differentiation to show why the derivative of a" is a In a, where a is a real number. Show all steps of your work. (b) Use logarithmic differentiation to find the derivative of e"g©os(x).
8 log, 4-3 Using rules for derivatives, find the derivative of f (x) sin a
plz provide answer for question part d and e Asap
e4 help pls
If false explain why.
A function h is dependent on x and is differentiable for all real numbers. Let g be the inverse of h. Part A: Use the derivative of inverse functions rule to write an expression for g' in terms of g, h, and x. Part B: Use the table of values to find g'(1). 1 2 3 h(x) -43 1 h'(x) 3 -1 4 X
= Calculus BS I Physics Home Insert View Review Pen (-x' if x1 then it has a) Removable DC (b) Jump Dc (c) Infinite Dc (d) Removable and Jump DC 10. The definition of the first derivative of a function f(x) is a) f(x) = f(x+Ax)+f(x) (b) f(x) = lim Ax-0 f(x+Ax)+f(x) (c) f(x) = f(x+Ax)-f(x) Ax Ax Ax f(x+Ax)-f(x) (d) lim Ax-0 Ax dy 11. Given y = 5e* + sinx, is dx a) 5e3* + cosx (b) 15e* + cosx (c) 15e*- sinx (d) 2.6666e* + cosx 12. f(x) = , is f differentiable on the given interval a) (0,2) (b) [0 ,2) (c) (-∞ ,) (d) [-o , o] 13. The Tangent line of y = sinx is horizontal at the point 3n a) x = tn, ± 2n (b) x = = (c) x = + (d) x = 2 + Tin for any integer n 14. x² + y? = 25 ,at point (1,-2) tangent line is a) x-2y = 5 (b) 2x-y = -5 (c) 2y-x = 0 (d) x-2y = -5 15. sin(re) = dr then de a) cose (c) 등 (4) ¿cos'e (b) Full text: 2406

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS

estion: Find the derivative of the following 1. function: y = In vtan x