QUESTION 3 dy Find - for the following functions. dx a) xy' +4x - y = x (Hint: Implicit differentiation) b) x= 8e* : y= cos (41) (Hint: parametric differentiation)

Q: Where does the graph of the function y=3•cos¬lx-sin¬'x have a horizontal tangent line? Provide an…

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Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Use..U. substitution. to. find each antiderivative. -48x 5-3x4 dx -3-

A: *to find:- integral value of the given function using substitution method.

Q: 4. y = 2Cos(x)Sin(2x) – Sin(x)Cos(2x) %3D

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Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

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: y = sin³ x cos x sec 4x y = tan 4x

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Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: 6. What does the following identity tell us about the derivatives of sinx and cos-x? sinx+ cosx =5

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Q: Question D. Use implicit differentiation to find all the derivatives. 1 3yz? - cos 4z – 3y² = 4 xyz…

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Q: Find an equation of the tangent line to the graph of the equation at the given point. x2 + x arctan…

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Q: Question:4 Calculate by implicit derivatives (tan x)" + ycotx + sinxy – exy – In2 = 0 - dx

A: The given function is tanxy+ycotx+sinxy-exy-ln2=0 Now, we find the derivative of each term…

Q: 5. Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.…

A: Given eq. is xcosy=1Now differentiate wrt x on both sides:ddx(x*cosy)=ddx(1)We know that…

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: 1-sin(x) (1-Sinx)2 10. Find the equation of the line tangent to the graph of y = 3cos(x) at the…

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given, y=coshtan-13x

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

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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

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Q: 17. Use Implicit Differentiation to find an expression for dy/dx given ry +y = 2.

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Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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

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Q: What is the derivative of 0.50 sin 2t+0.30 cos t

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

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Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: Find the derivative of sin 0 f(e) = 1+cose 1 + cos O 2)

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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: Page 5 > of 6 ZOOM 9. State whether the following is true or false by differentiation. [sin?(x) dx =…

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Q: Question 18 Find the derivative of y = tan (3x) [sec (2x)]-1 3 cos (2 x) – sin (6 x) sin (3 x) A cos…

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Q: Find the derivatives of the functions

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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: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

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: Question 2: Compute the derivative of y = arcsin(cos(arctan(r))).

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Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: Find the 2nd derivatives of y with respect to x   lnxy=x^(2)+cosxy(Picture below for reference)

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Q: Problem 2. Use implicit differentiation to find of ysin(xy) = y² + 2

A: 2. The equation is given by y sinxy = y2+2                              ........(1) To evaluate :…

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

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

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

Q: cos 2x-cos 4.x Express f(x) = using factor formulae. Hence, determine sin 2.x + sin 4x dy of y =…

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Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: y = k2 (Arc sin) – xvk2 – x² where k is a constant.

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Q: 1. sin?(ešin*t) + cos¯'(2t³ – 5)

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

Q: 1. Which differentiation rule is used to show ? -? sin y = cos y dx dx

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Q: Show complete solution. Determine the slope of the tangent line to the graph of the equation ey =…

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Q: 33. Зе - х%3D 0, (3,0)

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