Find the rate of change of the distance between the origin and a moving point on the graph of the function below if dx/dt = 9 centimeters per second y = x² + 7

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Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: 0 to x = 5 Determine the average rate of change of the function y = sinx from x =

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Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. xy = 8,…

A: Find dydx by implicit differentiation.Then find the slope of the graph at the given point.   xy=8…

Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (If an…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. x3 +…

A: Find dy/dx by implicit differentiation

Q: Find dy/dx by implicit differentiation. x = 2 In(y? – 35), (0,6) dy dx Find the slope of the graph…

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Q: Find dy/dx by implicit differentiation. x = 2 In(y? – 48), (0,7) dy dx Find the slope of the graph…

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Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

Q: Calculate dx/dy for the equation y4 + 1 = y2 + x2 and find the points on the graph where the tangent…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.      xy…

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Q: x sin(2x). (a) How fast is y changing at x = n? Let y = (b) Find an equation of the tangent line to…

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Q: Find the derivative of the function y = coth−1 (e2x)

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Q: Calculate dy/dx Simplify y=3x-5/2x+4 dy/dx=

A: Solving by derivative we have

Q: Calculate *xyz) dz dy dx.

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: A town library estimates that, when the population is x thousand persons, approximately y thousand…

A: A town library estimates that, when the population is x thousand persons, approximately y thousand…

Q: Find dy / dx by implicit differentiation. Then find the slope of the graph at the given point.

A: Given: x3+y3=6xy-1, 2,3 For finding dydx, we differentiate given expression with respect to x

Q: Find the derivative of the function y = (1/2) arctan e2x

A: Given function is y=12tan-1e2x Chain rule of differentiation states that: ddxfgx=f'gxg'x And also we…

Q: Find the average rate of change of f from 0 toπ/2 . f(x)=sin( x/2)

A: Derivative of a function determines the change of one variable with respect to another variable.…

Q: The acceleration of a particle moving along the x-axis is given by a(t) = (1-8)sint for 0 ≤1≤ 8. At…

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Q: The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: find the rate of change dy/dx where x=x0 y=x(1-x); x0= -1

A: We have to find rate of change of  y=x(1-x)at x=x0where, x0=-1

Q: 17. For f(x) = x*, the instantaneous rate of change is known to be –32 at x = -2. Find the equation…

A: the given function is f(x) = x4 rate of change dydx=-32,          at x =-2

Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: Calculate dy/dx Simplify y=x^7 (1-x)

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Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: 29. Differentiate the following implicitly to find dy/dx. Then find the slope of the curve at (1,…

A: Given: x3+y3=9 To Find: Differentiate the following implicitly to find dydx.Slope of the curve at…

Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. x3 + y3…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.     y2…

A: y2=x2-49x2+49 Differentiating with respect to x, we get…

Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

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Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: Find dy/dx using logarithmic differentiation. y = (8 + x)3/x, x>0 dy dx II

A: y=8+x3xTake natural log both side ,ln y= ln 8+x3xln y = 3xln 8+x ∴ ln ab= b ln a

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.…

A: Givenx3+y3=6xy−1Differentiate w.r.t…

Q: Differentiate implicitly to find the slope of the curve at the given point. 2) x2 + y2 = 1; (2, 3)…

A: We will solve the following.

Q: Consider the function Y3x2-6×+ス a. Find the slope of the tangent lihe to the curve at x=2 be Find…

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Q: Determine the average rate of change of the function y = cos x from x = 4 77 to x = 4 v2 V2 2 2

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.…

A: Given function is x+y3=x3+y3. To find dydx and then slope of the graph at point -1,1. Solution: We…

Q: are

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

A: The given expression is,

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Q: 1 c. y = 4 sec÷x 4 Arctan 2x d. y

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Q: Find the rate of change of y with respect to x at the indicated value of x. y = csc(x) – 4 cos(x); X…

A: Given that y=csc (x) - 4 cos(x).   ; x=π6 let’s find y1

Q: Differentiate the function. 1 y3= (2x +3) dy dx

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. x3 + y3…

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Q: Find dy/dx using logarithmic differentiation. y = xx − 8,    x > 0

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