If f(r) = cot + tan -1 4 -¹ (-) prove that f'(r) = 7² +4

Q: Let 1(2) = sin(rz) (1- h)? + k :>: (a) Find values of h and k so that ƒ is a differentiable…

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Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) > 0 and f"(x) <…

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Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

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Q: Let f'(x)= = f(x) = x² tan ¹(7x)

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Q: find I of implicit function sec""cImcy)- In(8**) when yoo

A: 9999

Q: Let f(x) - 9 sin' a 4 f'(x)

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Q: Find f such that f'(x) = f(x) = √x¹ f(1) = 13. ***

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Q: f6) =V20x (?,) f'G) f'(x)

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Q: If f (-4) = 0 and f "(-4) = 6, what can you say about f? Step 1 The Second Derivative Test says that…

A: f'(-4) = 0 , f'(x0) = 0 f''(-4) = 6 , f''(x0) &gt; 0

Q: unction fis given by f' (z) =-3z +4 for all z, and f(-1) = 6. Which of the following is an equation…

A: Given that the drivative of the function f isf'(x) = -3x+4  for all xand f(-1) = 6Now, f'(x)x = -1 =…

Q: (0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

A: From the graph,when 0≤x≤L, f'x=F Therefore, f(x)=∫f'xdx=∫F dx=Fx+cc being an integrating constant…

Q: tan x If f(x) = 3 sec a f (2) = f (1) =

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Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

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Q: Let f(x)=1/x^2+1 Find f'(1) Write the anserw in decimal form

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Q: Which interval is f increasing when f' (x) = x³ - x ? (a). (-00, 0) (b). (–1,0) (c). (–1,1) (d). (0,…

A: If f'(x) &gt;0 then f is increasing.

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Sketch the graph of ƒ. Include all important features of the graph: such as x and y-intercept,…

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Q: Q3\ Find the derivative of the following function by using the definition f(x) = X-1

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Q: Let ƒ(x) = − 2 sin¯¹(e8²) ƒ'(x) =

A: Given query is to find indicated derivative.

Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No…

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Q: In each part, list the points (A–F) on the graph of f whose x-coordinates satisfy the given…

A: Given data: The given graph is shown. Point A on the graph has zero slope and maximum value of the…

Q: Find all extreme value (if any) of f(x)=3x^½ + x, on the interval [-1/27, 1/27]

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Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: Evaluate / tan*(x) sec*(x) dæ.

A: I=∫tan3(x)sec2(x)dxsubstitute  tanx=udiffrentiatesex2xdx=du

Q: f(x)=2(9)^(x+1)=5 on what interval is the function positive

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Q: Let f: ℝ → ℝ by f(x) = 1 + x^2 and g: ℝ → ℝ by g(x) = 2^x + 3, calculate the following: (f ○ g)(1)

A: The composition of f and g is defined as: