Suppose f E C" (IR). Show directly that a fixed point xo is exponentially stable if f' (xo) < 0 and unstable if f' (xo) > 0.

Q: Find the first derivative of y = e3x. 3e3x

A:

Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

A:

Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: 3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = x

A: The given function is, y = x.Take log on both sides of the function.

Q: Compute the derivative in terms of log for y=log(xe^(-3x))

A:

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: Find the derivative of y =log2x

A:

Q: In (In e*1): What is the derivative of y 3z²+1

A:

Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) -1 1

A:

Q: Which of the following is the third derivative of y, if * y = (sinh 5)x2

A: we have to solve the problem

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

Q: In 5 x+1 Find the derivative of y = logs ((*)) with respect to x-1 independent variable x.

A:

Q: (3) Compute the derivative of the function e2t cos tdt.

A:

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

A:

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function: y=etan t Differentiate the above function w.r.t 't' dydt=ddtetan t The function…

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: y = log,(4x - 8x)

A:

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: What is the derivative of y = e3 In(5 + e3)? %3D

A:

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

A:

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: In (1 + 2), What is the derivative of y .? e2z %3D

A:

Q: In (6x) Find the derivative of y with respect to x if y = sin (3e) dt.

A: the given function is: y=∫0ln(6x)sin3et dt we have to find the derivative of y with respect to x.…

Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

A:

Q: Find and sketch an exponential equation of the form y = Ce^kx that passes through the points (0,8)…

A:

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: 2. #49: Compute the derivative. log3(sin(t)) dt

A:

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

A:

Q: 3. Find the derivative of (x² + 3) (3x – 3)² Y = Vrez+1 Hint: Use logarithmic differentiation!

A:

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

A:

Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

A:

Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x&gt;1 at x=10

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

A:

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: