Compute the derivative of Sin x in two ways: (i) Using the chain rule. (ii) Taking the derivative of the series for Sin x and comparing it to the series for Cos x. Express your answer in terms of the Cos function.

Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the d formula for…

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Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d² dt² -8 cos²…

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Q: (c) Find the derivative of nh (cosu). Where n is 482

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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: Find the value of x7 in 3 decimal places (positive value) using Newton-Raphson Method (7th…

A: To find 7th approximated root of f(x)=sinx-x using Newton-raphson iteration method.

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Compute the derivative cos(sin(e7))

A: cos(sin(e7)) We need to find the derivative of the given function.

Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Find the derivative and show your complete solution of the following 1. cos(e ^ (2x) + e ^ (- 2x))…

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Q: Use Newton's method with the specifled Initial approximation x, to find X3, the third approximation…

A: Newton's Method :If xn is a approximation solution of f(x) = 0 and if f'(xn)≠0 , then the next…

Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: Find the derivative of k(a)=sin^2a(cos^8a) k′(a)=

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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: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Find the derivative d/dx of the following 1 log sin(x)

A: We can find the derivative as below

Q: Use the tangent line approximation to evaluate the following in two ways. First, find the tangent…

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Q: by using Newton Raphson method; find the root of f(x) = sin x – e-x In the interval [0,1] for 4…

A: given f(x)=sinx-e-x       ; 0,1                since root lies in the interval   0,1     we choose…

Q: Use differentials to approximate the value of cos 29°.

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Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

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Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Find a real root for x tan x+1 = 0 using Newton Raphson method.

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Q: Find the derivative of   n^[ ln(cos u) ]  . Where n = 744

A: We will use logarithmic differentiation and chain rule of differentiation to find the derivative of…

Q: Apply Newton-Raphson method to determine a root of the equation cosx- xe^x correct to three decimal…

A: Let us consider an eqaution f(x)=0 with the initial point x0 to determine the roots of the equation…

Q: Solve for the value(s) of x over the interval 0 < x< 360 sin(2) = - V3

A: values=?

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: -1/7 17 dx =?

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Q: find the fourier series for the half-Periof sine of the function fxj = sinx inthe period x Then find…

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Q: Express ∫ sin x2 dx as a power series.

A: The given integral is ∫sinx2dx

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

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Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Find a root of f(x) = 6 Sin (x)e- x + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: 3. Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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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: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Find the equation of the tangent line to f(x) 16e* cos2(x) at x 4 (Use symbolic notation and…

A: To determine the equation of the tangent line.

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: f(x) = sinh x cos x,-n <x< n. ometric series.

A: fx=sinh x cos x , -π≤x≤π P is periodic of period 2π fx+2π=fx   sinx+2πcosx+2π=sinh x cos x  cosx…

Q: c) Find the derivative of nh (cosu). Where n is 482

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Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

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Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

Q: converges or div rge 2n+ Sinln)

A: The given series is  ∑n=1∞ 12n+sinn We have to check whether the series converges or diverges.

Q: Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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

Q: The approximation of the root x* of the function f(x) = ln(x + 1) - x + 3 accurate to within 10-2…

A: Introduction: Another recursive technique for approximating the polynomials' roots is the secant…

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

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