Explain the relation between the following two formulas (c is a constant): d sin(cx) = c cos(cx), dx a sin(xy) = y cos(xy) ax

Q: e (a cos bx + b sin bx) a + b? ax Secos bx dx=-

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1…

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Q: 1. Given f(x, y) = e sin(x² + y² ), find -2x and ôxôy ôyôx

A: Given: f(x,y)=e-2xsin(x2+y2)

Q: using the substitution u = cos(x). cos (x) sin(x) dx = +C

A: We have to find the integral ∫cos5(x)sin(x)dx

Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: _x²+y? f (x,y) = e' 3 (sin(x²) + cos(y²)) %3D %3D 3

A: Given function  fx,y=e-x2+y23sinx2+cosy2 fx=e-x2+y232xcosx2+sinx2+cosy2-2x3e-x2+y23…

Q: dx sin x cos x

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Q: :? If sin(x +y) = xy, what is the correct expression for dx cos(x+y) - y x- cos(x+ y) A cos(x + y) -…

A: for this problem, we can solve this by using general implicit  differntiation.

Q: What is F(x) = [ COS X √sin x dx? O F(x) = 2√sin x + C

A: NOTE: Refresh your page if you can't see any equations. . ...................(1) substitute…

Q: Given f(x,y) = 3x sin(3xy). Find fx(3,2). Give you answer correct to two %3D decimal places. Answer:

A: Topic:- partial derivatives

Q: 187. [T] f (x) =1+ cosr, x = 3元 2. COS I,

A: Given: fx=1+cosx The tangent line is to be found at, x=3π2

Q: f(1, y) = cos cos y is = COS I COS y

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Q: If (x) = tan(e"), then f"(x)= %3D A. 2e sec (e") B. 8e tan(e") C. 4e sec (e") D. 8e" sec (e*)tan(e")…

A: Given, f(x)=tane2x

Q: Given f(x,y) = 3x sin(2xy).  Find fxy(3,3). Give you answer correct to two decimal places.

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Q: Given that f(r) = sin z cos2 r + 2 = (sinx + a)² + ³ , the value of the constant and the least value…

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Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1) (A) 1/2 B)…

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Q: Explain the relation between the following two formulas(c is a constant):d/dxsin(cx) = c…

A: Given, ddxsin(cx)=c cos(cx)∂∂xsin(xy)=y cos(xy)

Q: Given f(x,y) = 4x sin(5xy). Find fxy(5,3). Give you answer correct to two decimal places.

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A 1 B)…

A: Given that ∫x sinx cosx dx=fxsin2x-gxcos2x+C

Q: The solution to the equation is * y'(x)- 2y'(x)+ y(x)-cos(x) slad Ja sin(x) - y(x) =c,e" +e,xe"…

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Q: Given f(x,y) = 5x sin(5xy). Find fxy(3,3). Give you answer correct to two decimal places. Answer:

A: Given :       f(x,y)=5x sin(5xy) To find : fxy(3,3)

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

A: Given∫a cos x dx

Q: Given f(x,y) = 5x sin(3xy).  Find fx(4,2). Give you answer correct to two decimal places.

A: fx(x,y) is partial derivative of f w.r.t x

Q: Find the value of dʻy/dx at the point defined by the given value of t. x = 5 sin t, y = 5 cos t, t=…

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Q: Given f(x,y) = 5x sin(3xy). Find fxy(4,2). Give you answer correct to two decimal places.

A: Given: f(x,y) = 5x sin(3xy). We have to find fxy(4,2).

Q: Differentiate the expression y = e* cos x²

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Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: dy da = y+ Vx² – y? O y = x cos(ln|æ|+ C) O y = x sin(n|x| + C) sin-1 (를)-In|미=C coS-1 (2) -Inl피 =C

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

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Q: y = In tan(x – A) +B

A: Some Important Formulas 1. ddxtanx = sec2x2. ddxsin-1x = 11-x23. sec2x = tan2x +1

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

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Q: Determine if the following statement is true. If it is false, explain why and correct it. For each…

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Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a)…

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 1/2…

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Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: Determine whether the following statements are true and give an explanation or counterexample. d. a.…

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

Q: Simplify your expressions for xM(t) = 0.5 cos + 9cos ( & ym(t) = 0.5 sin + 9sin xM(t) = B cos(kt +…

A: xM(t) = 0.5 cosπt3 +9cos πt6yM(t) = 0.5 sin πt3 + 9 sin πt6 XM(t) = B cos(kt + β)YM(t) = C sin(kt +…

Q: b) y = cos Vx

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Q: Explain the relation between the following two formulas ( c is aconstant):

A: Consider the provided formulas, ddxsincx=ccoscx   and   ∂∂xsinxy=ycosxy Explain the relation between…

Q: Given f(x,y) = 2x sin(2xy). Find fxy(3,3). Give you answer correct to two decimal places. Answer:

A: Given : Function fx,y = 2x sin2xy   To find : fxy3,3?

Q: Verify directly that the relation y = C3 e cos bx + c4e sin bx satisfies the equation [(D – a)² +…

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Q: . Consider the function f(x) = cos(0.6z). %3D i. For the argument of cosine, 0.67. to vary by 2T,…

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Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: For the equation y" + w?y = 0, Show that y(x) = A sin wx + B cos wx is a solution for all values of…

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A 1/2 B…

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Q: If f(x) = (e'7 cos(x))' 18e +12 sin(r) f'(0) then %3D f(0)

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Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: Determine whether the statement is true or false. 4 '1 (x2 + Vy) sin (x?y²) dx dy < 9 1

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Q: Consider J x sinx cosx dx = f(x) sin2x-g(x) cos2x + C. What is the value of f(1) + g(1)? A) 1 B) 1/2…

A: We have to find the integral