topic: inverse hyperbolic functions  If h(t) = sech2(et) then h'(t) = -2etsech(et)tanh2(et)   true or false

Q: sec z- tan zr sin a sec a

A: To verify the identity:- sec x - tan x . sin x = 1sec x

Q: Use Theorem 1 to derive the formula.

A: Given  ddxsinx=cosxddxcosx=-sinx The trigonometric identity used here is  cot x=cosxsinxcosecx=1sinx…

Q: Derivatives of hyperbolic functions Compute the following derivatives. a. dº/dx*(cosh x) b. d/dx(x…

A: Differentiation is the rate of change of a function with respect to a variable and differentiation…

Q: d 1 11. (-) dx x A.

A: The given function is f(x) = 1/x f(x + h) = 1/(x + h)

Q: The equation of the tangent line to the curve at the point (0,4)                 4+6x=sin(xy2)+y

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Q: 3 d 2 (x²) dx

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Q: Finding the derivative of trigono metric y = sin x cos x %3D

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Q: Evaluate the limit.

A: Given limit: limh→0 sin2h sin3hh2

Q: QI- 1) Show that cosh²x – sinh?x = 1 ii) Find the equation for the tangent line to the curve y = V+1…

A: By using the definition of hyperbolic functions in terms of exponents we solve (i) .  And by using…

Q: sin 2h sin 3h lim h2

A:

Q: sec 2a cos ydy - (1 sin y) da = 0 %3D

A: Given:     sec(2x) cos2y dy-x(1-siny)dx=0 Re-arranging sec(2x) cos2y dy-x(1-siny)dx=0sec(2x) cos2y…

Q: Using implicit differentiation find dy/dx if e^x-y=cos y

A: We have, ex-y=cosy   In implicit differentiation of a function of 2 variables, we differentiate the…

Q: 8. h (х) — 9 — 8 sin on [-3, –1]

A:

Q: Differentiation the function y = sin( – 6x)cot(- 7x) | y' = 7 sin(–6x) cos ec2(-7x) -6 cot(-7x)…

A:

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: sin(x+y) - coty siny sin X

A: To evaluate the given expression.

Q: Reflection: Across Line y = -x YA

A: When a point is reflect across line y=-x then x-coordinate and y-coordinate changes places and also…

Q: Sin 2x- Cos 2.x Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: See the attachment

Q: What is the slope of the line tangent to the cardioid in Example 2 at the point corresponding to θ =…

A: The equation of the cardioid is r=1+sinθ.

Q: Derivatives of Trigonometric Functions dy Using the formula find dx 4. y-sin (x + 3x + 1)

A:

Q: Derivatives of inverse hyperbolic functions Compute dy/dx for each function.a. y = tanh-1 3x…

A: we have to take the derivative of the inverse hyperbolic functions Compute dydx for each function.…

Q: Y = cose y = sine %3D -360° -360° -330° -330° -300° -300° -270° -270° -240° -240° -210° -210° -180°…

A:

Q: xy = e2*; y ху e2x; y

A:

Q: If y(x) = uv, then y' is *

A: This is an example of Product Rule of Differentiation

Q: Directions: In implicit differentiation, we differentiate each side of an equation with wo variables…

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Q: sinar lim,-1 r-1

A: Given limit is  limr→1sinπrr-1 Evaluate the limit. limr→1sinπrr-1=00 indeterminate form

Q: sin³ 350at

A:

Q: ACTIVITY 3: THE IMPLICIT DIFFERENTIATION Direction: Find Dy by implicit differentiation for the…

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Q: 2. Determining Advanced Derivatives of Trigonometric Functions A. f(x) = sin x + cos x B. f(x) = sin…

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Q: sin 5z-sin 3z 14. lim,» +0 sin z

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Q: derivative of the hyperbolic function below.

A: The given question is taken from the derivative in which we have to find the derivative of the given…

Q: Find the limit

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Q: 2y3 8. lim y-0 y-siny 9. lim(secx + tanx)csc X+0

A: To Find: 8. limy→02y3y-siny9. limx→0secx+tanxcscx

Q: d 8. -(2х) dx

A:

Q: sin x dx using Fourier transform. æ(x² + 1) -00

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Q: y = sech(x² + 2); y ||

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Q: fy=sin-¹ find Zy

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Q: y = 5-2x; y'

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Q: Find the derivative. (The Fundamental Theorem of Calculus- Part 1) 19) у %3D cos /t dt COS

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Q: 6.) eat cosh (be)

A:

Q: 1 d a (х 5. dx 2

A: It is the basic differentiation formula.  d/dx ( x^n) = nx^n-1  , this formula  is use to solve it.

Q: domain of g(t)= sin(et-1)

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Q: sin(2h)(1 – cos h) h2 lim

A: Consider Then simplify the function

Q: 4. f(x) = In cosh (4x)

A: The given function is, f(x)=lncosh(4x) Then, differentiate by the chain rule is,…

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x

A: The given question is taken from the calculus in which have to find its second derivative of the…

Q: d (2х* Зх 3) dx

A: Using basic differentiation formulae: ddx2x2    3x     3=d2x2dx     d(3x)dx    d(3)dx

Q: Find Derivative Using Fundamental Theorem: 1. Use Part 1 of the Fundamental Theorem of Calculus to…

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Q: cos (x+ y) cos (x-y) cos2 x- sin2 y

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Q: 25e230t sin² 40tt

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Q: Subject find derivatives of the first derivatives involwiny differences and. Zuotients. y=x sin'x…

A: Find the attachment