X Incorrect. (d) H' (4) if H(xr) = G(F(x)) H' (4) = eTextbook and Media Hint X Incorrect. F(x) (e) H' (4) if H (x) = G(2) H' (4) =

Q: y = In (x* + 5)³

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Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: 3.

A: Indefinite Integration

Q: 5. Find the first derivative of y = (2x³ – 1)5Vx² – 1 %3D

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Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

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Q: 5. Second derivative of y = 1+t)< t2

A: Given: y = 1+t2t2 To find: Second derivative of the given function.

Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: When the graph of the derivative is positive then the graph of the antiderivative will be…

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Q: What is the first derivative of f(x) = ln 3z²+7z ?

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Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: 1 Find the first derivative given that f(x) = xdx +

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Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: In (In e*1): What is the derivative of y 3z²+1

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Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: 13. Find the second derivative y “ of y = 5z2 +sinrcosz

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Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: What is the derivative of: y ln x − x ln y = 1

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 &amp; h=0.002

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

A: To solve the following problem

Q: Find the second derivative if y = sinh- (n + x') at x = 0

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Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

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Q: What is the difference of antidifferentiation and anti-derivative?

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Q: 2 Find the derivative of y = arctan(x´ + 3)

A: We have to find the derivative of the given function.

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

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln3/x

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Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: 4) Find the derivative of y = arctan(x² + 3)

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Q: Compute the derivative ln(ex+1) / 2x+1

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Q: Find the differential of the function y=lntan2x at x=π/8.

A: Given: ,at x=π/8 Differentials are infinitely small quantities. Use the term for differentials as…

Q: Find the derivative of the function.

A: Given

Q: 3 +Ve³ .2 3x e: f(x) =

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Q: 1 erivative of x²+2

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Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

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Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: 10.Anti-derivative of y(2y^2-3)^5

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Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: Find the second derivative of y=x-1 at x=2

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Q: 4. Find the 2nd derivative of f (x) = 4-x x)%3)

A: To determine the second derivative of the function given by; f(x)=4-x Differentiate the function…