Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y = (4x csc 3x2) (cot x4) 3. y = 2x - 1 / cos x2

Q: - a. Find the derivative of 3y – 2xy² = sin x + cot y b. Find the derivative of 2y x(3³) – In(²/²) =…

A:

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: 6. Use implicit differentiation to find the following derivatives for the equation tan y = 4 +x?y +…

A: see below the calculation and answer

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: 1. Given that x cosx dx = x sin x+ cosx + C By using the differentiation, verify that the given…

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: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: (sinsex + cos ty) = 58 coS xy) = 58

A: Given that: sin(πx)+cos(πy)7=58 Here, there is x and y variable, thus we need to perform implicit…

Q: 4) fip by implicit differentiation, where Find dr y + x?y³ = x* + y.

A:

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

A:

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

A: Differentiate y w.r.t x.

Q: 1 3.| y = xSin(x) + (1 – ÷x²) Cos(x) (1-**) Cos(x)

A:

Q: 4. Find the derivative of the following function. 1+ sin x 8(x) = 1+ cos x

A:

Q: find the derivatives with use of trigonometric functions 4 y = sin 2xcos' 3x tan 2x y = 1- cot 2x 3…

A:

Q: What is the derivative of sin? x f(x) = with respect to x? COs x

A:

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: The third derivative of y = sin is 1 -sin b) y" = --cos 1 а) у 8. 2 2 c) y" =-8sin d) y" = -8 cos

A:

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: Find the derivatives of the functions y = x2 sin4 x + x cos-2 x

A:

Q: 19. y = sin-1+ cos-1 2 2

A:

Q: Find the derivative of the trigonometric function. y = sin(3x2 + cos x)

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

A:

Q: Find a formula for y" (the second derivative) if y = 2* · sin x.

A: Given that, y=2xsinx            ...(1)

Q: 2 cos x 4. Consider the function f(x) = x2 find its derivative

A: Given function: fx=2cos xx2Differentiate the above function w.r.t 'x' f'x=ddx2cos xx2

Q: Find the derivatives of the functions y = 1/sin2 x - 2/sin x

A:

Q: 1-cos 4x Find the derivative of y sin 4x

A:

Q: Find the second derivative of the function. f(x) = sin(2x?) %3D f "(x) = 16x sin 2x) + 4 cos 22)

A: Given f(x)=sin(2x2) Formula: Derivative of sinx  = cosx Derivative of cosx = -sinx

Q: Let p and q be integers with q> 0. If y = x°, differentiate the equivalent equation yª = x°…

A: To show that the formula is true,

Q: Find the derivatives of the functions

A:

Q: Find the derivative of the given function: 1. y = --cot3(2x) + cot(2x) + 2x 3 secx 2. у %3D 1+tanx…

A: We have to find derivative Cot x = -cosec² x  Tan x = sec² x Cosec x = -cosec x cot x

Q: Sin X I+ COS f' (x) =>

A:

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: b) Use implicit differentiation to find for the equation yz? -e** cos (4zx)–3y² =4. F. DO NOT use…

A:

Q: 1. Find the derivative the following functions y=-10x+ cosx y=x'sinx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find y' and y" by implicit differentiation. cos(y) + sin(x) = 1

A:

Q: 3. Find the derivative y'(x) implicitly. cos?x + cos²y = cos (2x + 2y)

A:

Q: 8) Use implicit differentiation to find y', given cos(x+ y) = y² sin x

A:

Q: Find the second derivative, y" for the function cos(y) + sin(x) =1 by implicit differentiation. %3D

A:

Q: Q1/ Choose the appropriate function for this derivative sin x cos x V1+ cosx 2/1+ cos x

A:

Q: What is the derivative of y = 8 cos x? -16 sin x -8 sin x 8 sin x 16 sin x

A: In this question, we need to find the derivative.

Q: Find the derivative of the trigonometric function. y = 5 cos(  x)2

A:

Q: b. Find the derivative of y = Scos (x) sin(3–2x) + tan2(3x² – 4x) – csc(V2x – 1 Jand express your…

A: To find the derivative of below equation

Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find

A:

Q: 1+sin 2x 1) Find the derivative of f(x) = 2 cos x

A: To find The derivative of given f(x)

Q: Find the derivative of y=(e^2x)sin(5x)

A:

Q: 1. sin?(ešin*t) + cos¯'(2t³ – 5)

A: Solution: ddxsin2(esin2t)+cos-1(2t3-5)

Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x