Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar. whene is the graph of the original function, f lx), eoncave down ?

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: Compute the derivative of h(sin(x)) at x = pi/6 assuming that h'(u) / u =0.5 = 18. d/dx h(sin(x)) /…

A: We have h(sin(x))

Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

A:

Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

A:

Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

A:

Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

A:

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A: We will do all three parts.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = In(cos(In 0)) %3D

A:

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

A:

Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating…

A: Given that

Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

A:

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

A:

Q: Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) =…

A:

Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

A:

Q: sin 0 cos 0 1+ 2 In e y = In

A: Consider the function:y=lnsin θ cos θ1+2 ln θ   =lnsin 2θ21+2 ln θ…

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A:

Q: MY The derivative with respect to x of the function y=-3tan-¹x-(In 3) log, (csc x) is y' = cotx + O…

A:

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

A:

Q: What is the first derivative of the expression (xy)^x = e? Hint: this involves implicit…

A:

Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

A:

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

A:

Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

A:

Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: The domain of the function shown here is [Select ] The derivative of f(x) DNE at x=-1 because […

A:

Q: 1. y = cos2(2x − 1)

A: " Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

A:

Q: Find an equation of the tangent line to the graph of {(=) = [. t cosh (t² – 1) dt f(x) /1+ln (x)…

A: First I have written the rule of derivative of an integral to find the slope of tangent line for…

Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

A:

Q: Let f(x) = In(1 + 7 x). Find flS(0), that is the third derivative of f evaluated at 0. f(3 !3D

A:

Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

A:

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: