Use chain rule to find dz/dt z=cos(x+2y), x=6t^3, y=7/t

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: dx/dt = 2 and y=x^3, what is dy/dt when x=-4,2,6

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Q: A curve passes through the point (2,0) has gradient dy at point (x, y) that satisfy the dx equation…

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Q: Find the derivative of In(3t³ – 2t + 1) and then calculate S; + 3 dt (use integration by…

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Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

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Q: Ssin" x 14 x cos' x dx Integrate:

A: Given,        ∫sin14xcos5xdx

Q: The deferential of point functions are exact differentials. Select one: True False

A: True

Q: first derivative y= 4in Gty) is dy 4.

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Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: Prove the formula.

A: Given a function Arc Sine Hyperbolic (t). We need to find the derivative of the function. Let's…

Q: Find dy/dx by implicit differentiation   4Cos x Siny  =1

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Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Integrate:  (5e^-3x - cos (6x))dx

A: Integrate

Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

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Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

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Q: Integrate SxIn x)dy

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Q: Calculate the derivative: + (2t3 – 9t) dt = dz

A: Evaluate the given derivative as follows. ddx∫0x2t3-9tdt=ddx2t44-9t220x=ddx2x44-9x22-0

Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

Q: Find the derivative of In(3t3— 2t + 1) and then calculate  ∫ (9t2-2/3t3-2t+1) + 3 dt (use…

A: Given         ln(3t3-2t+1)

Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Find dy/dx by implicit differentiation 7ysin(x2)=9xsin(y2)

A: Find dy/dx for the implicit function

Q: How is integration by substitution related to the Chain Rule?

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us…

Q: Integrate  dy/dx sinx=1

A: We know, ddxcosec x = -cosec x·cot x ddxcot x=-cosec2x ddx(cosec x-cot x)=-cosec x·cot x + cosec2x…

Q: dy cosx+ ysin x =1 dx

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Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

Q: sec Vn du in

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Q: The integrating factor of Y + 3y cscx= cotx is?

A: Consider the given differential equation, y'+3ycscx=cotx This is the first order linear differential…

Q: dx 2.

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Q: A particle is moving with S. H. M. while making an excursion from one point of rest to another, its…

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Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

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Q: The integrating factor of Linear differential dy equations + y × 4 tan x = sec²x is dx . O tan 4x O…

A: To find the integrating factor for the below linear differential equation. dydx+y×4tanx=sec2x

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

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Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

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Q: find the differential dy if y= sqrt(2x^5-3x

A: Given query is to find the differential of the expression.

Q: ex dx

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Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: dy Find by using Chain Rule for y = sin³4t dt

A: Here we do u and v subsitution to get the derivative of given function.

Q: Calculate the derivative: d/dt ∫ from 1 to tan(t) of sin(x^2)dx=

A: Here the function is of the form:

Q: S(2x% + 3x -1)dx - 3x –1 dx Integrate

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Q: Find dy/dx by implicit differentiation. бх3 + x2у - хуз %3D9 y' = %3D

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Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

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Q: Find dy/dt of y=(1+lnx)/1-lnx

A: consider the equation

Q: Find dy/dx by implicit differentiation. 5x^(3)+x^(2)y-xy^(3)=-8 dy/dx=?

A: We are given an implicit equation as

Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

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