(3x2+5)8x-92 fy(1x4 + x2 logarithmic differentiation gives y (32+5)(8r-92 1x44+x2 16 2x 3x2+5 6-x9 6x 2x 16 32 5 8x-9-1+x 4.x2 (3x2 58x-92 (1+x)44x2 6x 16 4 2x 3x2+5 8x-9 1 x 6x 2x 16 3x258x-9 1+x 42 8r3-3x2+4r 1 (1x)(4x2)2

Q: y + 5xy + y = 6 ln x + 4 where y (1) = –1, y (1) = 1 (x-1)4 (x-1)7 -1 + † + | 12 504 + ... -1 + x –…

A: Taylor series expansion of f(x) about x=a is…

Q: f'(x) (11 + x)2 -V11,V11 VIī, VIT EX =p 7 of 7 2x(x² – (11 + x2)3 Substitute x = -/11, 11 in the…

A:

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is %3D Log(-12). O 2i -12 None of them O…

A: We have to find Derivative using definition and L'Hospital Rule.

Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: -3 Find the derivative for the function f(x) = (5x-4 + 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A:

Q: Find y’ when y^2 e^2x = 3y + x^2 and y(0) = 3 a. -5 b. -7 c. -6 d. -4 e. -2 f. -1 2. Find the…

A:

Q: Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be:…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 4x-3, 15. What is the derivative of f(x) ? Зх+2 17 a. (3x+2)2 4x2-3x b. 3x2+2x С. 16 d. (3x+2) 16.…

A:

Q: Suppose the function V represents the number of people vaccinated for COVID-19 in Kalamazoo country.…

A: Given : V represents the number of people vaccinated for COVID-19 in Kalamazoo country. To…

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 9-2a æ f (x) = 5xe®- Find the Critical Points Find where the first derivative is equal to 0. Enter…

A:

Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

A:

Q: g(x) = 2x^6-5x^4+3x^3-x^2+8x-9

A: Given: g(x)=2x6-5x4+3x3-x2+8x-9 To find: The nth derivative of the function.

Q: -what is the second derivative of i (-1) when i(x) =x^2f(x) -What is the derivative of g(3) when…

A:

Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: Question 5 Find the derivative [f(x)]; f (x) = 3 ln (In (x²-3x + 5)²). O3(2x-3) ²-3x+5 3(2x-3)…

A:

Q: 2. a) Find and fully factorise the derivative of f(x) = (2x + 1)2 using expansion and the power…

A:

Q: A relationship between (y – 2) and (x – 1) is given by (y – 2) = ab(x -1). . With a suitable linear…

A:

Q: 3x+7x What is the first derivative of f(x) = In(A? 5x Select the correct answer below: Os) = 6x-7…

A: Topic:differentiation

Q: 4. j(x) = {x3 - 2 <x <1 x² + 2x -4 x21 Domain: Range: j(-3) = -6-5-4 -3-2-1 0이 1234 5 1- -2 -3+ = ()…

A:

Q: Find the derivative of 3 -8-5-5 6 -2 0 5-5 1 f(x) = det-1 0 0-28 %3D X -6-9 1-3 0 0 0-4 O A-…

A:

Q: 4. The derivative of In (x2+1) is In (2x). 5. The derivative of In (x2+1) is 2* 6. The first rule…

A: 4. Given statement is the derivative of lnx2+1 is ln2x. Finding derivative of lnx2+1.…

Q: EXAMPLE 2 Find the derivative of the function below. g(x) = 3 + t2 dt SOLUTION Since f(t) 3 + t2 is…

A: To find the derivative of the function

Q: Find the derivative of this complex equation using logarithmic differentiation?

A:

Q: 1. Find the derivative of the expanded function  a. a^2x^2+2abx+b^2 b.…

A: 1. a) Given, a2x2+2abx+b2 Consider,  y=a2x2+2abx+b2 Differentiate with respect to x,…

Q: МАТ 115 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1) %3D с. f(x) d. f(x) = 4e*- x 3D20…

A: As per barlteby guideline for more than one sub question asked only first three are to be answered…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y…

A: As per our company guidelines we can answer only three subparts question at a time, but if you need…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A:

Q: -5-0 using Iterative fixed-point method by 2. Find one root of f(x) x+ choosing initial value as -2…

A: Given that fx=x3+4x2-5=0 To use iterative fixed point method to find one of the root of the above…

Q: 1 Find the exponential function f(x) = a* that passes through the point - 3, 216 and has a y- -…

A:

Q: 1 f(x) = 1+ 2x near x = 0: 1 1+2z 1 (b) Using your answer to (a), what quadratic function would you…

A:

Q: Differentiate the function. A) f(x) = 6x ln(8x) − 6x   b) (x) = sin(9 ln(x))   c).  f(x) = log2(8 −…

A:

Q: In (x + 3* V-1) Differentiate: h(x) %3D Differentiate g(x) = 3x+2 Use logarithmic differentiation to…

A:

Q: 7) Chapter 2.6 Find the first four derivatives of f (x) = 6æ³ – 2x² +1

A:

Q: 14. 2. loga(r) +3. loga(y) 13. 3. loga(1) + 3· loga(y) – 2 · loga(z) 16. 2+ log6(r) – 3. log6(y) 15.…

A:

Q: 64 = x 98. log5 625 = x 99. 1og3 104. e-2r+1 = 13 1 102. e2x = 3 101. e = 10 103. e2r+5 = 8 105.…

A: We use logarithmic properties

Q: ation. X 10- 3. 0.00052 = 4. 8,300= 3D x 10- oKT. 5. 7,000,000 = x 10- T 6. 0.0041= x 10- 8. 82,000…

A:

Q: Given the functions:  y = -2x+22 ,  y=−38(2^x)+24 a) Decay factor b) Decay rate c) Initial value

A: Consider the equation

Q: Find the derivative of: h(x) = (3x-2)/(x^2+2)   3/(2x) (-3x^2+ 4x + 6)/(x^2+2)^2 (-3x^2- 4x +…

A: The solution are next step

Q: . If 3 + f(x) = vx - 2 + 5x2, then (f'(x) is 2. Find the first derivative of the function f(x) = k ,…

A: Let's Solve,

Q: At time t = 0, there is one individual alive in a certain population. A pure birth process then…

A: A pure birth process gives the successive birth times as 25.8, 42, 52, 55.8, 59.2, 63.3. The process…

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

A:

Q: Find the derivative of: h(x) = (1/x^2 - 1) / (1/x -1)   (1/x -1)^2 –1/x^2 (1/x^2 – 1)^2 (1/x +1)^2…

A:

Q: Find the derivative of: y = 4x^2 – 1/x   y’ = 2x – x^(-2) y’ = x^(-1) + 8x y’ = 8x - x^(-2) y’ =…

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

Q: Overtaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B…

A: (a)

Q: Find dydx by implicit differentiation, given that x2y−3y3=−1. Your answer could involve both x and…

A: We differentiate both sides with respect to x We use the product rule for x2y

Q: Example 2. Find the derivative of the following with respect to x. x" +1. (iv) x-5 (i) x12 + 7, (ii)…

A:

Q: 5V3 6. Question 9 Find the derivative of (8 x + 1)*. a) O (8 x + 1)* (3 In(8x + 1) – - 8x + 1) b) O…

A: