Q57.a) Find if y=sin(tant) and t=cos(x) dx

Q: Evaluate: J x?cos(2x)dx

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – 2) =…

A: Given: Let z be defined implicitly as a function of x and y by the…

Q: Q5-Find for x? + cos(xy) = y dx

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Q: cos-1(2 x2)

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Q: If z = x?y + 3xy, where x = sin 2t and y = cos t, find dzidt when t = 0.

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Q: dy Find if cos(xy) = x2 + y?. Show your work. dx

A: Differentiate wrt x

Q: d Q 3. Prove that tanx dx sec?x. =

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Q: Se Ce cos (sin '(x)) COs (sin

A: We need to find the antiderivative of ∫ecossin-1xdv

Q: If u = tan -1 x- the value of x2 +y?+xy du at x = 1 and y = 3 is

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

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Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: B) Find (dy/dx) for the following 1. y = tan2(cosx)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 4. Find when dx tanx a. y e, giving your answer as a function of y. b. y- In(xvx-1), x> 1 sinx-cosx…

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: 1 dx x +c, find- dx exactly where c is a constant. 5. If 1+cos x = tan 2 X 3+3 cos 4 n dx tam S c /+…

A: It is given that

Q: B) Find and if x sin 3z and y = tan 3z dx

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Q: When |x3 cos(x?) dx is evaluated using IBP, the value of v du is? cos(x*) - cos(x³) -cos(x*)

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Using an appropriate substitution, f sin (x)cos (x)dx is equal to:

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Q: a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

A: To find dy/dx.

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: 2 x If y = x¯e" sinx,Find d

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Q: Find by definition for the following : dx 1. y = (2x² + 1) 2. y = cosx 3. y = sin?x

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Q: Evaluate in x cos x dx. .3 I COS" T

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Q: Q2: Evaluate: * Jx* sin(1- x)dx?

A: use substitution method to solve the integral

Q: d²y for 15 = cos x Find dx? cos x + a°y?

A: We need to find d2ydx2 for 15=cos x+x3y2. Let us differentiate both sides.                    0=-sin…

Q: Differentiate the following function. y sin 11x y' = cos (11x) 11 %3D

A: Consider the function  y=sin11x

Q: dy is: If y = tan(47x²) then dx

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Q: a)- Find for, (x+ y)* = tan-14x + + Inlny !! dx

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Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: d dx et ex sin x + e* cos x

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Q: Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

A: Given: fx=sinxcos3xf'x=cos4x-2sinxsin3x To find: f''π3=?f'''π3=? Formulas used:…

Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Q9.a) Find if y=sin(tant) and t=cos(x) dx

A: We can solve this problem using chain rule.

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: Prove that d/dx [cos x] = −sin x.

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Q: H.W Find y' for y = ecosx tan- (5x) * (5x² + 1)? COS

A: Given,           y=ecosx*tan-15x*5x2+1

Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…

Q: d le" cos.x) cOS x dx

A: Given ,  d/dx(ex cosx)  We know that  d/dx(uv) = u'v + uv'  Here ,  u = ex and v = cosx Then ,

Q: (b) If y = sin (m sinh¯x), find the value of (yn)o ·

A: Hi, you may find the answer in the form of hand-written note.