Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

Q: Find the differential dy of the given function. (Use "dx" for dx.) dy =

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2nx - 1 cos 2 dy = ||

A: topic - derivative and differential equation

Q: Find the differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y? + z²; x = psin o cos…

A: We have to find derivative of given function by using chain rule.

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: If z + In(e2x - e + e²) = 0 dz find at the point (0, 0) dx 2 0 -3 -2

A: see below the calculation and answer

Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x² = Ap

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Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

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: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

Q: If the PSD of X(t) is S„(@). Find the PSD of dX(t) dt

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Q: Find the differential of the function. z = e ** cos(8nt)

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Q: Find dx/dt: x = 2[cos (t/2)]^2

A: x=2cost22

Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

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

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: Find the differential dy of the given function. y = ln sqrt 5-x^2 dy=

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Q: g(x) - (x)/ A.If f(x) = dt, where g(x) = + sin(tº )]dt, find f'(÷). (1

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Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: x dx = e* + cos x e* + sin x O a. In(e* +sin x)+C O b. In(e* + cos x)+C О с. - In(e* + cos x) + C…

A: To evaluate  ∫ex + cos xex + sin x dx

Q: 5. y = l 1- co s x 1+co s x

A: We have to find out dy/dx for given y

Q: Find the differential dy of the given functions . (Use "dx" for dx.) a) y = 2x − (sin(x))2 b)…

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt

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Q: By referring to implicit differentiation techniques, compute dy at point dx (3, t) for the following…

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Q: find dy/dx. g(x) = cos x/sin2 x

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -5x – (sin(x))² dy =

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Q: The given identity sin(s + t) = sin s cos t + cos s sin t. Compute the partial derivative of each…

A: The given identity sin(s + t) = sin s cos t + cos s sin t. Compute the partial derivative of each…

Q: Find the derivative. cos X d 78° dt dx 1 a. by evaluating the integral and differentiating the…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x2

A: Use  the differential of the form f = u.v

Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: use the integrating-factor method

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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