find dydx 15. y = (sec x + tan x)(sec x - tan x)16. y = x^2 cos x - 2x sin x - 2 cos x17. ƒ(x) = x^3 sin x cos x 18. g(x) = (2 - x) tan^2 x

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

A:

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Use integration by parts to verify the reduction formula.

A:

Q: Find dy/dx by implicit differentiation   4Cos x Siny  =1

A:

Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

A:

Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

A:

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: 3. S. 2 cotx-3 sin²x dx sin x 4. (2x2+x dx x+1

A:

Q: (2x-2) dx sinx dx 2. 3. √xdx 4. J² (²2x²+4x-2) dx 5. So (cosx+tanx)dx 1/1/4 6. Jo ¹/2_dx =dx √1-x²

A: Solve by integration

Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: d arctan (tanh x) dx Show that sech 2.x.

A:

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

A:

Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

A:

Q: Differentiate f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

A:

Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

A:

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

A:

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: find integral sec 3 x dx

A:

Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find dy/dx 1. y = x^2(sin^−1 x)^3 2. y = e^tanh x/x^2 − sechx 3. y = tan^−1 (sechx) + sech(tan^−1…

A: We expert are following guidelines.We are supposed to do first question. We have to find dy/dx

Q: 8. The value of f sinh* x cosh³ x dx

A:

Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

A:

Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

A:

Q: 1) y = sin(1 – x²) 2) y = tan 'Vx² + 2x 3) y = tan1 Vt²-1 + csc 1t

A: Given the trigonometric function

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: Solve x - cos(x) = 0 by Secant method. Use x-1 = 0.5 and xo = 1.0 as the initial estimates. %3D

A: We will find roots till 4 digit repeat

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

A:

Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

A:

Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

A:

Q: Find dy/dx of x siny + y = 4x + 3

A:

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

A:

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)

Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

A:

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

A:

Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

A:

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

A:

Q: Determine the maximum/minimum point(s) for y=sin 2x– cos x – 4x on the interval 0 <x< 2n . The…

A:

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

A:

Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…