Suppose f and f' are differentiable functions of r. Given f' (=) = 0, f" (4) = -1, and g(x) = log sin(2r) + v2f(x) + cos find g" () %3D

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: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find the differential dy of the given function y=extanx

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Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

A: We need to find out : 7)  dydx if y=4exx 8) First derivative of f(x)=sin2(x3)

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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

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Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: 2. Evaluate the integral: | sinh x cosh² x dx

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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…

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Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

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

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Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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

A: Given function is rewriting in other variables as: y=x(sin(ln(x)))+cos(ln(x)) Product rule of…

Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: If e (3x + 2)e2* dy 3 4 using logarithmic differentiation. (b) show that +2 2.x-1 %3D (2x-1) dx 3x…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: It can be shown that the Difference Quotient (D.Q.) of f (x) = sinx is h-[sinx(cos(h) – 1) +…

A: We are provided that the Differential Quotient (D. Q.) of f(x)=sinx is h-1sinxcosh-1+cosx sinh, if…

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

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

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Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

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Q: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

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: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

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Q: Solve for the derivative of the given implicit functions. a. Find dy/dx for y= ln (4x+tan-1(lnx)).…

A: Solve: a. Find dy/dx for y= ln (4x+tan-1(lnx)). b. Find dy/dx for y= tan-1 (3x-2 sinx). c. Find the…

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

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

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

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)…

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Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

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

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Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

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Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.