A mining expert estimates that the production growth rate of copper overtime, or "/dt, is given by dy -3t?y + 6t? dt where, y is copper production and t is unit of (continuous) time. The mining expert would like to determine the level of copper production overtime (y(t)). Given the above information, answer the following questions:

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: The equation of tangent line of the function 21 x3 f(x) = e7e dt %3D 21 x at x=1 is V21 e3087 (x-1)…

A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Another particle has a velocity function of v(t) = [' 2'-* dx. What is the acceleration of this…

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Q: Find the derivative of the given function. y=cos(e^-5theta^3)   dy/dtheta=

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Q: Find the derivative of y = = Ve-5t +1 dy dt ||

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Q: You would like to use differentials to approximate the change in BMI when weight increases from 55…

A: Given: The function represents body mass index(BMI) is  Bw,h=wh2 where, w means weight in kilograms…

Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

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Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: Find the derivative of y = 7 In(sin t + 5). dy/dt =

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Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: Compute dy/dx for the function. 2. y sinh - 6x

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Find the differential d3y of the function y=xsinhx.

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Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: Given y=2x2+1 , dxdt=2 centimeters per second .A point is moving along the graph of the given…

Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

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Q: Find the derivative of the function. s=? In |t| ds dt II

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Q: 5. – 3t te dt

A: The given integral is: I=∫t e-3t dt

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: Find the differential of the function. y = sqrt(1+ln(z))   dy=?

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Q: If z = (x + y) e and x = 6t and y = 1 – t, find the following derivative using the chain rule. Enter…

A: In this question we have to find the differentiation of z with respect to t.

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: Can you help me step by step with this problem?

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

Q: Find the differential d3y of the function y=1/√x.

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Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: The derivative of the function y 1 = COS Va at a = 0 is equal to

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Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…

Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

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Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

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Q: A 15 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding…

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Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

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Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

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Q: Let x > 0 and b > 0. Show that

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Q: Calculate the increment and differential of the function y=x2−x+1 at the point x=2 when dx=1.

A: Given, the function is y = x2 -x +1 at the point x = 2 and dx = 1, We have to calculate the…

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.