Let I = f(x) dx, where fis the function whose graph is shown below. y f 2. 2.

Q: define y as a differentiable function of x,  find the value of dy / dx at the given point. (x3 - y4)…

A: Given : Define , y as a differentiable function of x . The equation is ( x3 - y4 )6 + ln ( x2 + y )…

Q: What is the range of the tangent function y=tan(x)? A R B [- 1, 1 [0, + ) D (- 00, 1]U[1,+ ∞)

A: Tanx is the ratio of sinx and Cosx

Q: c. f(1) d. Is f differentiable at x = 3?

A: Given The graph of function f as  To find: c. f1d. is f differentiable at x=3?

Q: find dy/dx as a function of x. y = sec (tan x) %3D

A: Given that  y=sec(tan x)2

Q: Find dy/dx and d²y/dx². x = t2 + 7, y = t² + 9t dy dx2 For which values of t is the curve concave…

A: Here we have to differentiate the given parametric equation.

Q: Find for the following functions: - dx 1- y = (Inx. Vsin x) 2- f(x) = xcos2x

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Q: dy =2xy with y(2) = 1. dx Find a function y = f(x) that satisfies

A: To find a function y=f(x) that satisfies dy/dx=2xy with y(2)=1

Q: dy for the function y = dx 7) Using the first principles definition, determine 2x

A: topic - derivative of a function

Q: Differentiate the function. 71 y=(9-x) 0 dy | dx

A: We can solve this as follows:

Q: dy as a function of æ. dx inction in the form y = f(u) and u = g(x), and then b. find Preview…

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Q: Find dy/dx and d²y/dx². x = et, y = te-t -t e + -te dy dx ーt -2e -t + te d²y dx2 For which values of…

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = tan3 x

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Q: dy for the following function: dx Find y = (x - 3 (1- x)

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Q: dy when x dx If f is a differentiable function and y = sin (f (x²)) , what is = 3?

A: Given F is differentiable functionand Y=sinFx2we find dydx when x=3

Q: dy The derivative for the dx 22 22 + 22 function y =

A: We use chain rule to solve this derivative

Q: Evaluate dy and Ay for the function below at the indicated values. y= f(x)= 44 1-- x- 2, dx Ax = -…

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Q: Find dy/dx and dzy/dx2. x = t? + 9, y = t² + 5t dy dx dy dx2 For which values of t is the curve…

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Q: dy Find for the function y = etanz

A: Differentiation

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

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Q: dy 3- Find dx for the following function: A- y = ecosv3x-1 B- y = x². secx

A: (a) Evaluate dydx of the given function as follows.…

Q: dy Given the equation 4x° + x²y - y° = 0, evaluate Assume that the equation implicitly defines y as…

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Q: Q3/ Find dy/dx at the given point for the following function

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: dy d²y Find and dx dx² x=t² + 4, y = t² + 9t 11 dx d²y dx² For which values of t is the curve…

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Q: Sketch the graph of y = v4-x², - 2<x<2. a

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Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)

A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.

Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = sec…

A: Function given is: y = sec(tanx) u represent the function inside and so u = g(x) = tanx Then y =…

Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: dy for the function dx The derivative y = 6. - +

A: We will find  the derivative dy/dx for the function  y . Here , we will differentiate with respect…

Q: Fx to find Fy dy dy Assuming 2x° - 8y + 10xy =0 defines y as a differentiable function of x, use the…

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Q: Consider the function f defined by y = 1/x a. Find dy and △y at x = 1 with dx = △x = −0.5. b.…

A: To consider the function y=1x

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

A: A detailed solution is given below

Q: dy for the implicit function x +y -2y = 3. Then find the equation of the tangent line at the Find dx…

A: use differentiation for finding the slope and then use it for finding the equation of tangent line.

Q: f(x+h)-f(x) = lim 1. Use the delta method, dx for the following: dx to find h0 2 BONUS MARKS y = 5x2

A: We will use the definition of derivative as defined in question.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. fix) =Dx + 는,…

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Q: Fx to find dy Assuming 8x - 9y - xy = 0 defines y as a differentiable function of x, use the theorem…

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Q: 6. y = (tanx + sinx)-3 %3D

A: To find dydx for the given function 6) y=(tan x+sin x)-3 The given function is the composition…

Q: dy Find dx for implicit function x? sin y + 3y3 = e5 + 5

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Q: dy Given the equation x? + 4xy +y° = 8, evaluate Assume that the equation implicitly defines y as a…

A: Given query is to find derivative of the given expression with respect to x.

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

A: The equation is 2x2+xy+y2-22=0 Differentiate this equation with respect to x…

Q: dy Given the equation y In (x* +y +5) = 7, evaluate Assume that the equation implicitly defines y as…

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Q: Consider the following function: y = x*. dy dz ||

A: The given function is y=xx2. Rewrite the given function as follows. y=xx2y=elnxx2y=ex2 lnx

Q: dy Find for the given function. dx 9 - tan(x) y 9 + tan(x) dy dx

A: Proceed as shown below

Q: The curve y= f(x) passes through the three points (1,3), (2,8.5), and (3,44). Estimate, as accurate…

A: The given problem is to estimate the first derivative of f(x) ,dy/dx at x=1.5 for the curve y=f(x)…

Q: dy Find of the following. dx 3t X = 1+t³ 3t² y 1+t3 t + -1 |

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Q: dy Find dx for the function y = ecotx

A: We want to find the derivative of the given function.    y=ecotx Here we apply chain rule of…

Q: dy Find for the following function: dx 1- y = etan'x

A: It is differentiation using chain rule.

Q: Find dy/dx and d²y/dx². x = 2 + 3, y = t2 + 3t dx d?y dx2 For which values of t is the curve concave…

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Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

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Q: Let f(x) = x^5+x^3+2x, and let g(x) be the inverse of f.

A: Given that,f(x) = x5 + x3 + 2xand g(x) is the inverse of f(x).