onsider a continuous function y- f(x) whose first derivative is y' 3z-2r. he function f has point of inflection at O a r b. None 3. Od r 0 Clear my choice

Q: F (x, y) = (cos x). (Sin y) - (cos y). Which of the following is the derivative of the function (sin…

A: Explanation of the solution is given below...

Q: (e) y = (x³ + 1)² () y = (x² +5)³

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Q: OC Find the derivative of the function y = dy dx dy 8 dx dy dx dy = - 8 x-4/5 ∞ 188 5 8 x-2/5 x 5²…

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Q: Find the indicated derivative. In this case, the independent variable is a (unspecified)…

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Q: dy using implicit differentiation dx 6. Determine (a) x²tan(y) = 2tan(y) dy answer: dx xsec2 (y) (b)…

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Q: Find the first derivative of the function f(x) = sin (x) . a) O f'(x) = 3sin?(x) b) O f(x) =…

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Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

A: y'=cost,    0≤t≤2π

Q: Sz 3. Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

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Q: f(r+h)-f(x) Using f'(x) = lim Find the derivative of f(x) COS T.

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Q: x In x Find the derivative of y given that y= 1+ In x - x In x A ex 1+ In x + x In x B ex 1- In x+ x…

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Q: Find the derivative of f (x) = In x- A. В. 1– x2 2 C. x2-1 D. x² +1 E. None of these 1- x2 Given the…

A: To differentiate the given functions.

Q: ey = (x² – 6x)² and its derivative - 4x(x - 3)(x – 6) to find each of the following. Find the…

A: Given that: y=(x2-6x)2 dydx=4x(x-3)(x-6)     NOTE: As per our answering guidelines, we can only…

Q: Find the derivative of the function. h(t) Step 1 Apply the general power rule which states that if y…

A: Given function as ht=t4t7+82

Q: uy For the function: sin y = 5x +9, find (using implicit differentiation) dx O -5 csc y Oɔ csc y O…

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Q: Theorem: If the equation f(x, y) = c defines y implicitly as a dy af 7 0, then dy differentiable…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, oo).…

A: Given,           Let f(x) be a function that is defined and has a continuous derivative on the…

Q: Calculate the partial derivative dw using implicit differentiation of w+x? = at (x, y, w) = (1,2,…

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Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h-0 s(x) = 4x + 2…

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Q: Let y = f(x) be a differentiable function. If the derivative of f is zero at x = a, then the…

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Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

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Q: f (x) dx = 7 The function f has a continuous derivative. If f0) = 1, (2) = 5 and x. f' (x) dx what…

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Q: derivatives fry and fyx are equal. f(x, y) = In (1 + x²y")

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Q: x²+3 Suppose y = and x = sin (u)ln (u) a. Determine dy using the first principles definition of a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 17.

A: differeentiate both sides with respect to x and solve the question. see 2nd step.

Q: Consider the function below: sin(a² +y) (x f(x, y) y-x (x Find the value of the derivative fr at the…

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Q: Take the function f(x) = arctan (x²). %3D (a) Find the average rate of change over the intervals…

A: Consider the given function. fx=arctanx2 The average rate of change is defined as, rate=fb-fab-a…

Q: Sx, if xe Q if x ER – Q. f(x) = Using only the definition of derivatives and Lemma 4.2.2, determine…

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Q: dy for xy+3x = 2cos(x+ y)-e" by using implicit differentiation. dx b) Find %3D

A: Given: xy+3x2=2cosx+y-e3y

Q: QI / Find dy/dx by using the definition of derivatives for the following functions; 1. y = 1. y = =…

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Q: 2(z–1) sinh z cosh I + 3(x – 1)'sech? (z)? Which among the choices will result to a derivative of O…

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Q: dz dz Find by implicit differentiation, and confirm that the and dy results obtained agree with…

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Q: 4. Let y = 5-2x be the tangent line to a function y = f(x) at r = 3 and y = 2+3x is the tangent line…

A: Equation of the tangent line y=f(x) at x=x0 is  (y-f(x0))=f'(x0)(x-x0)

Q: True or false? The function f(, y) is continuous at x² + y? the origin. O True False

A: We have to check three condition for continuity

Q: (x³ + bx + a, xs-1 lbx? - Let f(x) = .Then the values of a and b so that the %3D -a, x >-1…

A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x>-1 So, the function is continuous at x=-1 if…

Q: Find the first derivative of y with respect to x (y') of the given function.

A: Given function is  : x2y-xy2+x2+y2=0

Q: a) Find dx of the function y = (x+1)²using the limit definition of the derivative. b) What is the…

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Q: Pregunta 9 The derivative of y = (10*)/(In 10) is O a y' = (10^x)/(2 In 10) b y'= 1 y' = 10^x d y'=…

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Q: dy Find r by implicit differentiation given thattan(1 lx +y)= 11x. Use the original equation to…

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+y) =xy. What is…

A: We have to find derivative

Q: (a) Find the first and second derivatives of the following function (1² + x)(x² – x + 1) f(x) = %3D…

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Q: Find the indicated derivative. In this case, the independent variable is a (unspecified)…

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Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2). The graph of f has…

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Q: Q4: (a) Find Critical point of f(u) = ue" + Invu +n, Where n is 482. %3D (b) Find the increasing and…

A: Solution (a): We have to find the critical points of f(u)=ueun+lnun+n, where v=482. We get critical…

Q: ecosh z √x+1 Let F(x) S 1. Find F(0). 2. Find F'(x). sin(1 t) dt.

A: Let's find value of given function.

Q: Can i get help step by step please

A: Consider the given function Given that the function is differentiable on (0, 1) and satisfies f(0)…

Q: 3. Find the derivative of the following functions. Do not simplify your answer a) f(x)=x²sin(5x) b)…

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Q: f(x, y) = x²y+ e®r" sin(y), P= (2,0) Direction of fastest increase is Direction of fastest decrease…

A: Given Data: Function: f(x, y)=x2y+e6xysin(y) Point: P=(2, 0) The derivative of the function with…

Q: The derivative of the function y = tan-1 1+ csc-1 x, where x > 1 is: CSC y' = 0 y' = 1 %3D %| O the…

A: y=tan-1x2-1+csc-1x   where x>1