a(22) V17 – cos(2nt)" (2 – 4) sin() 1. Given f(x) dt, find the equation of the line tangent to the graph of f at z =.

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Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

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A: Given; ey+cosx=1 at point (π/2,0).

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Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

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Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

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Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

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Q: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

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Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: &y dy :5 cos t, the third order derivative dt For the function dt3 is 5 cos t -5 cos t -5 sin t cost

A: Here we will find 3rd order derivative

Q: (2 – 4t) sin() tan(2r) V17 – cos(2nt) Find the equation of the line tangent to the graph of f at r =…

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Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

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Q: Find the derivative of y with respect to 0. y = In (8 cos 2e) dy %3D de

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Q: dw H.W: Use the chain rule to find the derivative dt with x = cos x = cos² t, y = sin² == and…

A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: Consider y3-2x2=1+sin(xy)   a) Use implicit differentiation to find dy/dx.   b) Find an equation…

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Q: Given: f(x) = / (2 – 4t) sin() - dt %3D tan(2r) 17 – cos(2nt) Find the equation of the line tangent…

A: The tangent is a straight line to a curve that touches the curve at exactly one point. The point…

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: A particle moves along the x-axis with velocity given by v(t) = 57 sin (t) for time t>0. If the…

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to…

Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

A: For the given problem, there are two questions. But according to rules of Bartleby only the first…

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: Find an equation of the tangent line to the graph of {(=) = [. t cosh (t² – 1) dt f(x) /1+ln (x)…

A: First I have written the rule of derivative of an integral to find the slope of tangent line for…

Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

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Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.