IX. Find y' if 1. (5 pts.) y = 2 In (cos (Tx)) 2. (6 pts.) y = csc² (Arcsec (Va) + e-)

Q: Find dy/dx by implicit differentiation. (cos TX + sin Ty) = 18

A:

Q: Find y′ if y = tanh−1(sinh x2).

A:

Q: s sec(cosx) dydx siny

A: Given : ∫01∫sin-1yπ2 sec2(cosx)dydx

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

A:

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: 8. Find the principal value of Arc tanh(1 + j2)

A:

Q: Find the derivative

A: To compute the derivative of ln|cscx|

Q: L(cos(at)sinh(at))

A:

Q: Find the coordinates of the point on the graph of y = 8 sin x+4 cos (2x) + 14, 0 <x<5, where the…

A: Consider the given function, y=8sinx+4cos2x+14 The slope of the tangent line on the given curve will…

Q: Find dy/dx if y=(4/cosx)+(1/tanx)

A:

Q: S cos*x sinx dx

A:

Q: first and second derrivative of: y=Arccos(e^2x)

A:

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: 1. S sinh ) dx 2. S sech? (x - ) dx 3. [6 cosh (- Inx )-) dx

A: Since you have posted multiple subparts question in this question so I have solved first question as…

Q: Li S cos(x)esin(x)-2y dxdy

A:

Q: 1 of 1 че le y=sı sin find derivative eq uatlon of tangent Iine at t= Ò

A:

Q: Solve for the derivative Arc sin + Arc cos =0 y y

A:

Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

A:

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

A:

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

A:

Q: 4In(Arctan x) = 1-y

A:

Q: Evaluate the integrals

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 2. Use implicit differentiation to find dy/dx: e"y+ In(arcsin 2y) = 3ª ln y + 5.

A:

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

A:

Q: If y- sinhx then prove that dy dx

A:

Q: Find , if y = x sinh x - cosh x %3D dx

A:

Q: dy without first solving for y. dx Use implicit differentiation to find

A:

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: Va2-x² Y=Arc sin + а

A: Differentiate wrt x

Q: D/Dx (cosx)^x  slope of tangent function (cosx)^x at x=π/4

A: Given:- y = (cos(x))x To find:- Slope of tangent at x=π/4

Q: Find dy/dx by implicit differentiation 4 cos (7r) sin (6y ) 5

A: We have been given an implicit function and we are supposed to find dy/dx.

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

A:

Q: Find the slope of the tangent line to the sine function at the origin. y 2 y=sin -1 Compare these…

A:

Q: If y = 4 tanh x + sinh 2x, what is the slope of the curve when x = 2? Assume h = 0.5 and 0.01;…

A:

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: by implicit differentiation. 8. Find dx sin(xy) = 1+ cosy,

A:

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 1. y = Arcsin(- Vx²+4

A:

Q: Arc lenght of Curue y=ln(sinx) at intervol I sxS Ę

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)° = 24 dy/dx =||

A: Our objective is to find out the derivative of the implicit function.

Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

A:

Q: 10.y = Arc cot (sinh3x) 11. y = cosh?4x - cos 12. y = In (sinh4x) cosh8x +x² 2

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) /…

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

Q: 9. [sin Ssin' cos–dx 3 3

A: (9) To evaluate ∫sin5x3cosx3dx Substitute sinx3=u and cosx3dx=3du. Therefore,…

Q: Cualuate the definle integial. x33 COs (xH) dx

A: