Use forward-difference formula to evaluate the first derivative of y = cot(x) at x = using a value of h= 푸. %3D %3D 212 -4 2(v2–2) -2/2

Q: What is the derivative of `y=\ln\ x`?

A:

Q: Find the derivative of y = sin x³ cos x?

A: As per our  guidelines we are supposed to answer only one question. Kindly repost  others  questions…

Q: y = ln 1-x² 1+x²

A:

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: find the derivative of y with respect to the givenindependent variable. y = θ sin (log7 θ)

A:

Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: Find the derivative with respect to t. y= csc-1(et)

A: Given:

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y…

A: (21) Consider the provided equation, y=lncoshy-12tanh2y Find the derivative of y with respect to the…

Q: Find the derivative, if y = (log x)" +(sin x)™* -x %3D

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Q: What is the derivative of y = e2 +1, with respect to x?

A: Formula used

Q: Find the derivative of y=sinh-17x

A: Given:y=sinh-17xHyperbolic Identity:cosh2x-sinh2x=1Differntiation formula:ddxsinx=cosx

Q: Which is the second derivative of y=vx ? *

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Q: Find the derivative of the following functions:     1. y= 3 ln (x)?

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Q: Find the First Derivative of the Given Function: 2.) x=sec53t

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Q: 3. Find the second derivative of y= xlnx

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Q: y = In(tanh 2x)

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Q: Evaluate the derivative of y =e* sinh (2x). -3x

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Q: Find the derivative of y = sin(-* e-X 2ex + 1

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Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

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Q: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: 3. Find the derivative of y = csc" (sec x), 0<x< 2n.

A: Given ddx(arccsc(sec(x))Let sec(x)=uWe know that ddx(cosec-1…

Q: Find the second derivative of y = cot 3x

A: To differentiate the function in the first derivative as y' ordydx  and the second derivative as y''…

Q: find the derivative of y with respect to the appropriate variable.23. y = (x2 + 1)sech (ln x)

A: Definition used -             ddxsech(x) = -tanhxsechx          Product rule of derivative -…

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

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Q: What is the first derivative of s(æ) = 4e"*.

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Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: With respect to x, what is the derivative of: * H5 du -3/5 Option4 Option 2 2/5 du -3/s du dx…

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Q: Find the derivative of the function. y = tan−1 (square root of x - 4)

A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…

Q: Find the derivative of y = tanh e^(7x)

A:

Q: Find the derivative of the (e) h(x) = e5 sin (Væ) + a° sec ()-

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: Find the second derivative, dz2 where y is related to x implicitly by the equation below. 2x + 4y =…

A: we have to find derivative

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

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Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: Q3: find the derivative of the following: 1. y = lnx + √1-x² sech-¹x 2. y= sinh-1(tanx)

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

A:

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: What is the second derivative of y = sec “(3 x) ?

A: For the question 1, none of the options match. If the question had asked for first derivative of y…

Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

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Q: f y = (sin x)x b

A:

Q: Find the second derivative of the equation below evaluated at y = 1:

A: Given that: The implicit equation 4 e y + x y = 4e.

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: Calculate the derivative of the following function. 6. 6x y%3= 7x+1 dx

A:

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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Q: find the derivative of y with respect to the givenindependent variable.

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.