Find the range of the function x* +e x+e f(x)%3sin{log, +cos {log. x' +1 2 x*+1

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

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Q: Use implicit differentiation to find dy given y³2 – log(x²y¹) = cos¯¹(1). dx

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Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: FInd the intervals in which the function f(x) =sin(logex) +cos(logex) is decreasing

A: Given function is, f(x)=sin(logex)+cos(logex)

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: 3. Use properties of logarithms and/or logarithmic differentiation to find the indicated derivatives…

A: a.)  y =ddxlnx2   ⇒y =2ddxlnx =2x                                                  ln(ab)…

Q: 16. Use logarithmic differentiation to find y'. (a)= (x2 + 1)tan(=) (b) y = (sin (3z))VE

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Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

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

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

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Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Find the average rate of change of f from 0 toπ/2 . f(x)=cos(2 x)

A: Find the average rate of change of f from 0 to π2 .     f(x)=cos(2x)

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: 23: Find The Domain of the Function. y = sin (log, x²]

A: Given: y=sin-1[log4x2]

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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

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Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

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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: Find the derivative of y with respect to x. y=log(base)5 e^7x

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Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

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Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Find the derivative d (2* log2 x) dx

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Q: The derivative of the function y = cos(x In 3) log3(sin x) is:

A: Given,            y=cosxln3log3sinxTo find : The derivative of the given function.

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

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: 2. Use Logarithmic Differentiation to find dy/dx for y = 3 x(2x+5) (x²+1)²

A: Explanation of the answer is as follows

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

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Q: i dont understand a) through c)

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

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: Find dy and simplify whenever possible. dx 1. y = arcsin + 4-x2 2. y = In(e¯* + xe¯*) sin x cos x…

A: To find derivative of given function.

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: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

Q: Find the derivative: 1+e5 f(x) = = COS 1.

A: The given function is f(x)=cos1+e5x1-e8x

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

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

A: Given, d2dx24 log2x-5