6) In(x²) = (ln x)²

Q: y = In (x* + 5)³

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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: 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 of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: Show that √(10x + 1) and √(x + 1) grow at the same rate asx→ ∞ by showing that they both grow at the…

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Q: Compute sinh(ln 5) and tanh(3 ln 5) without using a calculator.

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Q: compute the derivative f (x) = ln(4x2 + 1)

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Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: Define in your own words   Differential equation

A: Differential Equation: Any equation which contains derivatives is called the differential equation.…

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

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Q: 17 0 in QII 32. sec0= - mot 15

A: Given:secθ=-1715,  θ in quadrant 2

Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: 2 cosh(2x) – sinh(2x) = 2

A:

Q: Solve for Xi 31 In x =D 늦 (Inle t 21n2) %3D

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Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: find derivative y=square root of (1+ x times e^-2x)

A:

Q: Find the 3rd derivative of y = xlnx. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

A: Given : f(x) =y= x lnx To find : Third derivative of given function

Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

A:

Q: Differentiate the following function.   y = ln(3x+1) - ln 3

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: Find the derivative of function.

A: To fFnd:  Derivative of y=ln 4ln3x

Q: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce…

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Q: Compute the derivative of ln r3 –1 V2x+5x²

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Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

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Q: Determine the first derivative of the ff. function y = 400(2)*+3 sin 3x

A: Given: y=4002x+3 sin 3x To Find: First derivative of the given function

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: 3. Show that the differential equation zxy

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Q: 4 + sinh(3x) = 4 cosh(3x).

A:

Q: 4 Find the first derivative of y = In X +

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Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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Q: find the differential equation of the family of logarithmic curves whose equation is Cy = ln(Cx).

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Q: Can you provide atleast 5 average or complex examples of Ordinary Differential Equations?

A: I listed 5 example of ODE with answers.

Q: he first derivative of f(x) = ln(5X4 - 6x) will be

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Q: Find the second derivative of 2x^2 ln (1/x^2)

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Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

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

A: Use l hospital rule

Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

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Q: Determine which differential equation is linear:* (tan 2x)(")+(x-23)(»")' = In.x

A: A differential equation is linear only if it satisfies the conditions below. The degree of the…

Q: In( cosh(3x) - sinh(3x) )=

A: