Find the first derivative with respect to all variables

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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Q: find the derivative of the log functions: y = ln(x√x2 – 6) f(x) = ln(2x/x+1)

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Q: 1) Using method of logarithmic differentiation, find the derivative of y = (2.x² + 1)(2=-3)

A: Given: Y = (2x2+1)(2x-3)

Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: Suppose we want to use logarithmic differentiation to calculate the derivative of y=x²x . As a first…

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Q: find the derivative:  y = ln (8x^3 – 2x) – 2x

A: According to the chain rule of differentiation if fx and gx is the differentiable function then,…

Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: 2. f(x) = 3. g(x) = 5 In x – 2* 4. g(x) = 4x³ log, x

A: To find the derivative of the given function. 2). Given function is fx=x2ex. Quotient rule of…

Q: Find the derivative of function and simply it whenever possible y= ln(ln sec x)

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Q: 4) Use logarithmic differentiation to find the derivative Of the given fünction.Show all steps.…

A: Consider the given function y=xx1+x24

Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 5th derivative of y = log x^5 to the base 2

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Q: 5) Find the derivative using logarithmic differentiation: y = Xcanx

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y…

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Q: 6. Find 39th derivative of f(x) = sinh(x). A. sinh(x) B. cosh(x) C. – sinh(x) D. - cosh(x) None of…

A: Derivative of sinh(x) is Cosh(x) and  Derivative of Cosh(x) is Sinh(x).

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: y = (lnx)lnx Take log to the natural base e on both the sides to get,

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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Q: 7.) f (x)> (3x+2)(5x-2)

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Q: State the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the…

A: Given: fx=logbx for finding derivative of given function, first we convert it's base in e then…

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: 11) Find the first derivative of y = (lnx) 4

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Q: e3x _e-3x Y = e3x +e-3x]

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Q: Find the derivative of the function. f(x) = ln   1 2x8

A: Given,         fx=ln12x8

Q: 3) Find the second derivative of 2x f(x) = for x + 0 3x2+4x Show all steps. Simplify your answer as…

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Q: 4) Use the Chain Rule instead of the Quotient Rule. 4 Find the derivative y= 2x +1

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Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: find the second derivative and simplify the final result. 3. 4ln(Arctan x) = 1-y

A: The given function is 4lntan-1x=1-y It can be written as  y=1-4lntan-1x Differentiating with respect…

Q: Find the derivative of the function. h(x) = ln[(−6x + 3)(x + 3)]

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Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

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Q: 1. Use logarithmic differentiation to find first derivative of y = xsinx

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the derivative of the function. f(x) = ln(8x + 9)

A: Given, f(x) = ln(8x + 9)  We have to find the derivative of the function.

Q: Find the second derivative of the f(x)=9+8x ln x function

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Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),      (3,…

A: To Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),…

Q: Find the derivative of f(x) = ln(2x^3 + x).

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Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: The L'Hopital rule and The derivative of the exponential function. lim (ex + x³)*:

A: Use l hospital rule

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: Given query is to give an example of exponential and logarithmic differentiation.

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: Applying natural logarithm on both sides, we get

Q: Find the derivative of the function h(x)= ln(5x+1/7x-2)

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Q: Find the derivative of y = log7 (2 -3x) .

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Q: find the equation of the tangent line to the graph of the function y = ln(x^2) at the point (3, 1).

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Q: Find the derivative of the function. f(x) = ln(4 − x6) f '(x) =

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