. y=(cosh^-1(sec(3^x)))/log 3 Find: (y')(3^-x+1)

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: In(x) (1 point) Find dy/dx using the method of logarithmic differentiation when y = (5+3x²)**. dy/dr…

A:

Q: cosh(3x²y) = ln(e*y + 1)

A: Differentiate the cosh3x2y=lnexy+1 with respect to x. dcosh3x2ydx=dln(exy+1)dx Use the chain rule…

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

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Q: fx ln x dx.

A: According to the guidelines the first question can be solve in multiple question. Kindly repost…

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error 1…

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

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Q: 1) [(sinh 2x + cosh2x)° dx

A:

Q: | If In(x² – 3y) = x – y + 3 and y(-2) = 1, find y (-2) by implicit differentiation. y(-2) = An…

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Q: 2 cosh(2x) – sinh(2x) = 2

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Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

A:

Q: Use logarithmic differentiation to get the dy/dx of: y = (20^x) tan^-1 (x^2 - sinh 2) / (cosh^3 x)…

A: Use logarithmic differentiation to get the dy/dx of: y = (20^x) tan^-1 (x^2 - sinh 2) / (cosh^3 x)…

Q: The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then…

A: Let the side of the cube = s = 10 cmError in the side = ds = ±0.03 cmNow,Volume of the cube = V =…

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: | 25. a. Find a curve with a positive derivative through the point (1, 1) whose length integral…

A: a) Find the curve-

Q: 3. x)dx sin(ln

A:

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: In estimating | cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error…

A: We have to find the error in trapezoidal and Simpson rule .

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

A:

Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3.…

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: How is ln x affected if x is multiplied by et?

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: tanh 2x In (cosh 2x)dx

A:

Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: calculate the integral.

A:

Q: Solue this Logistic stochostic differentialegh where ajb,c constant wit) ;win er Process by using…

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Q: 3x-4 Y = Arctan

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Q: differentiation

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Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: Given,  The one side of a right triangle is 20 cm long and the opposite angle is measured as 30°,…

Q: Y = 2 Arccos ( 1 -) + v4x – x²

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Q: Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

A: given function

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: 8. Scoth 2x In (sinh 2x) dx

A:

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

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.