(a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh(x). (ii) cosh(x). (iii) tanh(x).

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: sinh2 (등)

A:

Q: The second derivative of the given function is - 5 sin (2- 5x) -125 sin (2 - 5x) 125 sin (2 - 5x) O…

A:

Q: 1. Find the derivative of each of the following: (a) y=e2* ln´(cos x) Do not simplify your answer.

A: We have to find the derivative of the function…

Q: 19. The function ƒ(x) = ex + x, being differentiable and one-to-one,has a differentiable inverse…

A:

Q: Find the derivative of the functions. (Answer Five only ) xIne 1- y = In x 2 In 5 In 25 2- y =…

A: In this question we have to find the derivative of the functionwe

Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 20. Find the derivative of the following functions (do not use exponential definitions of hyperbolic…

A:

Q: 3. (a) What is the derivative of sin(g(z))7 (b) What is the derivative of sin(2r + T)?

A: We have to find

Q: . h(x)= cot 1 -tanx

A: Given:hx=cot-11x-tan-1x

Q: 57 6. Find an equation of the tangent line to y = f(x) = cos²(x) at %3D

A:

Q: 6. Solve the definite integral ro e(arcsin(x)) dx. V1 - x2

A: the value of the integral is 1-e-π2 see below the answer and calculation

Q: B) Find the derivatives of the following functions: (for only 6) 5) y- In ( sin' 0) 6) y = log:() 7)…

A:

Q: (2) What are the derivatives of the six basic hyperbolic functions? What are the corresponding…

A: Hyperbolic functions are the trigonometric functions defined on parabola instead of taken on the…

Q: 44. Find the derivative of loga u with respect to x. a. log u du/dx b. u du/ln a c. loga e/u d. log…

A: Given data÷

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Q. Find for the following functions: - a- y = (cosx) (use logarithm differential) C- csc-/3/5x b- y…

A: we have to find the derivative of the following

Q: cos (2x) Find the derivative of cos(e2«)

A: Given that: ecos2xcos(e2x)

Q: What is the approximate value of the first derivative of the y = sinx function at x =pi/4 when you…

A: The first derivative of the function can be obtained using the forward and backward difference…

Q: 23: Find The Domain of the Function. y = sin (log, x²]

A: Given: y=sin-1[log4x2]

Q: 11. Consider the equation x + y +e# = e dy using implicit differentiation. dx (a) Find (b) Find the…

A:

Q: What is the relationship between the functions In r and e?

A:

Q: x² d. Find dx (e" -tant)dt. tan(x?) a. 2x(e** - tan(x?)) Ob. 2xex - sec?x O c. O d. It is impossible…

A:

Q: 3) e y = (cos x)" using Logarithmic Differentiation

A:

Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

A:

Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

A:

Q: 2x y= Arccos(e)

A:

Q: 3. Find the derivative of the given exponential function w e2t (2 cost + sin t)

A:

Q: What is the derivative of y log b ( cos? (ax) ? Note that a and b are real numbers. A - 2 a log ble)…

A:

Q: Question 13. Obtain the derivative of the function f(x) = 2 ln(4x) Enter the answer as a function of…

A: topic - derivative

Q: Find exact value(s) for x such that 3e" - e' = 0.

A:

Q: Breathing is cyclic, and a full respiratory cycle from the beginning of inhalation to the end of…

A:

Q: x2 + 1 Find a formula for the tangent line for y = at x = 1. x + 1 e rational function does not…

A:

Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

A:

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

A:

Q: 6. S(x)= In(tanh 5"

A: As per bartleby guidelines we only give first question answers.

Q: Differentiate the function.

A: Consider the following equation: y=e-2tcos4t Differentiate y with respect to t: dydt=ddte-2tcos4t…

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Q3) Find the derivative of y for all functions the following (1) y 0 (sin (In 0) + cos (In 0)) %3D

A: Q3) (1) Differentiate with respect to Use chain rule to find the derivative of y

Q: Disprove the statement ln(xy) = (ln x)(ln y) by, a) Letting y equal a positive constant of your…

A: We know the logarithmic formula for the product of x and y as: ln (x y) = ln x + ln y Let, ln x = a;…

Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

Q: 5cos³ (x) Find the derivative of y + tan²(3x² – 4x) – csc(v2x – 1 )and express your sin(3–2x) answer…

A:

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos*…

A:

Q: 1-x Find the derivatives of the following functions sinh' 1+x

A:

Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…

Q: ind the tangent to the föliüm of t what points on the curve of x' +y 6xy is the tangent line…

A:

Q: arc sin z = -i log(iz + V1- 22).

A: