Praw a slope field for the dtfferea- differentiation equation y = xty sketch an and approprlocte solution Curve pating through points y (1) = -3

Q: Consider the curve described by the relation y + eV= x* - x² + 1. Find an equation of the tangent…

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Q: 10. Find the first derivative of sin (y) + cos (x) = 1. cosx siny sinx a. y' b. y' %3D cosy C. y'…

A: We have to find the first derivative of sin(y)+cos(x)=1.To find the derivative we use chain rule of…

Q: %3D %3D y = In ( sinh 2z) Find the derivative of y with respect to z.

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Q: Show that the given femction satisties G-R Q. 4. conditions at origin but doesnot have a derivative…

A: Given we have given a function  f(z) = (x3-y3)+i(x3+y3)x2+y2,    if z≠0              0            ,…

Q: A.) use implicit differential to find (dy/dx)  B. ) Find the slope of the curve at the given point.…

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Q: Find dy/dx by Implicit differentiation. x = 9 In(y-15), (0, 4) dy %3D Find the slope of the graph at…

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Q: Example: show that u(t)=sin t i + cos t j+ 5k has constant length and is orthogonal to its…

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Q: find the directional derivative of function

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Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)= -2 ex cos (yz),…

A: Use directional derivative formula

Q: az Find dz by implicit differentiation, and confirm that the and dy results obtained agree with…

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Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

A: y'=cost,    0≤t≤2π

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)= -2 ex cos (yz),…

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Q: Sz 3. Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

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Q: Find the derivatives of the functions y = z sec-1 z - √z2 - 1, z > 1

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Q: Q.1 (i) calculate the following: lim(4x' –3x² –15) x' -4 lim x-2 (ii) An equation of a curve is…

A: 1. (i). Calculate the following...…

Q: 4a) Use differentials to approximate V9.7 . Round the final answer to three decimal places. 4b) Find…

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Q: se implicit differentiation to find hp without first solving for y. dæ æª + 3æ°y + y² = 15 ,10, dy…

A: Given: 5x4+3x10y+y2=15 Given query is to find the derivative and equation of tangent. The equation…

Q: Find the derivative of x2y? + x³ + y = 8 at (2,0). %3D Find the derivative of y = cot-2 (x).

A: 1) The given function is x2y2 + x3 + y = 8 and the point is (2, 0). Evaluate the derivative of the…

Q: u(1) = 2 and u' (1) -4. Find the tangent line to the curve и(х) cos(y) — 5eV — 3. at the point…

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e cos (yz), Po(0,0,0),…

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: 4a) Use differentials to approximate V9.7 . Round the final answer to three decimal places. 4b) Find…

A: [4B] *concept:- d/dx{cotx} = - csc^2{x} d/dx{x} = 1 d/dx{x^{n}} = n*x^{n-1}

Q: 14. Find the second derivative of tanh xy + xy =0 by implicit differentiation. A. y" =2 B. y" =2 C.…

A: Answer is option C)  y''=2y/(x^2)

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=2 ex cos (yz), Po(0,0,0),…

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Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: (4) (a) Find dv/dx by implicit differentiation: cot y = x – y (b) Use implicit differentiation to…

A: Take derivative with respect to x and express dy/dx in terms of x & y.

Q: Find the derivative of y with respect to x. - 1 y = csc (x- + 1), x> 0 dy %3D dx (Type an exact…

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Q: dz (3, –2, 1) if xyz + x³ + y³ + z³ = 14. dy 2. Find dz Hint: Use implicit differentiation to find…

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Q: Assume that x and y are both differentiable functions of t and find the required variables below.…

A: x and y are both differentiable functions of t y=x We need to find implicit differentiation dydt a)…

Q: a) Use your knowledge of derivatives and/or integrals to plot the velocity v(t). Assume the initial…

A: The given acceleration v/s time graph is The following can be understood from this graph:1. The…

Q: 2. Given that arcsec 2) + (x² – y²)² = 2. (a) Find dy using implicit differentiation. dx dy usino…

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Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: a) Use the Chain rule to find the derivative of z = e*y with respect to t if X =t cost and y t sin…

A: We will solve the following.

Q: Slope of a tangent line at t1 = 6.0 and y = at? dy v = lim At-0 dt

A: Given that: y=αt2

Q: Which order of differentiation will calculate fxy faster: x first or y first?  a. ƒ(x, y) = y + x2y…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

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Q: iven y = at / bt²+ct 31 find dy/dt where a, b, and c are constants. Find the slope of the tangent…

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Q: 오. x5 - y3 = 0, (1, 1) dy dr 2. At (1, 1): y' =

A: The given equation is  x5 - y3 = 0.... (1) To find dy/dx

Q: Consider the curve 3x? + 7y? = 1. Find y' by implicit differentiation. V = y' Find y" by implicit…

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Q: a) Find the first derivative of the followings: i) f(x) = sec²x tan/ã ii) f(u) = cos²(sin(1 – u)~1)…

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Q: dy using implicit differentiation. dx 3. Find sec (xy?) = (cosh x) (tanh 2+v9) + 2 csc-1 (tan(y +…

A: Implicit differentiation

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

A: Topic:- application of derivatives

Q: 2) f(z) = (« + iy)“ - i (x+ iy)

A: Given function: fz=x+iy2-ix+iy.   We know that if fz=ux,y+ivx,y is analytic then f'z=ux+ivx=vy-iuy.…

Q: ...] A particle moves such that its position at time t is given by +++)i+ G + 5° – t - 5) i+ ( -* +…

A: "Since you have asked multiple questions, we will solve only the first question. For the remaining…

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z=-2 1+x? ; d²z/dx? 2. Y = (3x3 + 2)ª ;y"…

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 e* cos (yz),…

A: We can solve this as follows:

Q: Use differential calculus to determine the exact position and nature of the stationary points for y…

A: We know that a stationary point of a function f(x) is a point where the derivative of y=f(x) is…

Q: Assuming that the necessary derivatives of ƒ(x, y, z) are defined, how are Di ƒ, Dj ƒ, and Dk ƒ…

A: To find the relation between the directional derivatives Dif, Djf, Dkf with the partial fractions…