dy y? y(to) = 0 2t dt

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

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Q: dz Find given: dt =ze, =t', y= 5+5t dz dt

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Q: dy sin(y + t) dt %3D

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Q: dx x2+y?, dt dy 2, find dt dL when x = dt If L = V -5, and 7 and y = 6. dL dt

A:

Q: Find dy/dt y=(40+e^t)ln t   dy/dt

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dx If y = 2x3 + 3x and dt dy 3, find when x = 4. %3D dt dy dt =

A:

Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: da dy 3x? – 1 and dt Find at z = 1 if y = at x = -5. dt da dt

A: topic - derivative of a function

Q: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

Q: Find dt y = 6t + /9+ 7-t dy dt |3|

A:

Q: Solve 12 dy dy ty = t®y=1 dt

A: A differential eqaution of the form y'+p(x) y=q(x) yn, n ∈ℝ is called a Bernoulli differential…

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: L{t}(s) = / t dt te -at %3D

A: Here we use integration by parts.

Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: dx Let y = 0.75a? + 4.25 and dt 0.6. dy Find when x = 3. dt

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Q: Let y=x^2 + y^2= 100. If dx/ft=2, find dy/dt where x=6 and y=8

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: d² y dy } +24% +y=sinh3t – 5 cosh3t ; y(0) = -2, dt² dt y (0) = 5

A:

Q: Find the general solution for y(t) where; dy a. dt + 6t?y = 2t2 dy b. + 10y = 0 dt

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Q: Find dy/dx

A: Given:y=∫0ex2 1t dtIntegrating formula∫xn dx=xn+1n+1

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: y = f VI + t? dt Y : 0. t2 dt

A:

Q: Find dy/dx: 1. y = J" cos t dt

A: Given

Q: If y = (t² + 2t + 6) (3t² + 5), dy find dt dy dt ||

A: Given function: y=t2+2t+63t2+5 We have to find dydt

Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

Q: dz Find given: dt Z = xe?", * = t“, y = 5 + 6t dz dt %3D

A: Put value in terms of the then differenciate

Q: Compute xe" dx + x?y dy along the curve x 3t, y = t2, 0 < t < 1.

A:

Q: 3 + 1)'0 dy calculate dx Given y = dt

A: From the fundamental theorem of calculus, ddx∫0xf(t)dt=f(x) And from the chain rule,…

Q: f(x,y)=sinx+cosy+xy2, where x=cost,y=sint Find df/dt at t=π/2.

A: We can find the answer as below

Q: dy Find dt y = (t sin t) dy dt

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Q: dx = 5x + y; dt x(0) = 2 dy -3x + y; y(0) = 0 dt

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Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: Find the general solution for y(t) where; dy а. dt + 6t?y = 2t? dy b. + 10y = 0 dt

A: The given question has been solved in detail

Q: dx dt dy dt x(0) = 2 y(0) = 1 3x – Y 9х — Зу

A:

Q: dy Find dt y = (t sin t)6 dy dt

A: Given: y=t sin (t)6 We have to find dydt: Consider, y=t sin(t)6=t6 sin6(t) To find dydt…

Q: e'dy + (5t + ye')dt = 0.

A:

Q: dy Find dt y = (21+ et) In t dy %D dt (Type an exact answer.)

A: To find the derivative of following function

Q: O1f y= x 4x and x = Vzr?+I, find dy /dt when t r2. %3D

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Q: dz Find given: dt z = xe²y, x = t³, y = - 5 + 6t dz dt ||

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Q: Please show all work

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Q: dz 2) Find if z = xy² + x?y, y = ln x %3D dt

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: