Let a be a real valued constant. Evaluate e-az sec(e¯a«)dx . O - In|sec(e-a*)+ tan(e¬a")|+C In/sec(e)+tan(e¯")| +C - In|sec(e-)+tan(e¯a=)| + C In|sec(e)+tan(e*)| + C

Q: Let f(x) be a function with domain (-00, 3) U (3,00). Use the graph of f'(x) below to determine the…

A: Step 1:

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: At what points are the functions in Exercises 13-30 continuous? 1 1 + 4 (x + 2)2 13. у 3x 14. y %3D…

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Q: In Exercises 61-67,firstfind f' and then find f.

A: To find f' and f. Given information: f''x=12x,  f'0=1,  f0=2

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

A: 9999

Q: 6 fla) 【うt+1} tx4)

A: given,        fx=3x4+1x3+4

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) > 0

Q: Find the derivative of each function. し-X a) f(x)=7x² tanx -1 %3D u du ol x v du そar1 (x)2x tan…

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Q: Evaluate: tan(x) dx

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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: x+ cos X Find the derivative of tan x . O A) tan x+ tan xsin x+ xsec x+secx tan? x tan x(1+sin x) O…

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Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

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Q: Suppose the distance (in feet) rest is given by the function f(t) = 3t ^ 2 (0 <= 1 <= 30) . a).…

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Q: Let f(z) be the principal branch of (z)^⅓, find f(-i)

A: What is Principal Branch: A function that chooses one branch of a multi-valued function is known as…

Q: In Exercises 61-67,firstfind f' and then find f.

A: Solution -    Given function -  f''(x)=x3-2x+1Given conditions-f'(0)=1, f(0)=0   a.) Evaluating…

Q: The chart below gives information about the derivative of a function f (x). f'(x) + + + +0---0- 4 0…

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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: What are the indeterminate forms and L'hospital's rule in application of derivatives?

A: We have to define Indeterminate form and L'Hospital Rule

Q: Evaluate / tan*(x) sec*(x) dæ.

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

Q: (4) Consider f(x) = x5 + xª + 1. (b) On what intervals is f(x) one to one? (c) Find a formula for…

A: (d) Consider a given function: fx=x5+x4+1 Let gx=f-1x. Find g'1.0488 when domain of f is restricted…

Q: Iff

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Q: f'(x) = f(x) = cos(2x + 3)

A: Given query is to find the derivative.

Q: CONSIDER A FUNCTION F: [-3,3] => R WHOSE SIGNALS VALUES AND THE DERIVATIVES ARE SHOWN BELOW. FIND…

A: Consider a function F : -3, 3 →ℝ, Given table is Intervals f f' f'' x&lt;-2 - - +…

Q: 3x Let f (x) = Then the derivative of f is 1 + 5x f'(x) = A(1 + 5*) – Bx(5*) lIn C_ (1 + 5*)D where…

A: Given: f(x)=3x1+5x To find: A, B, C, and D if f'(x)=A(1+5x)-Bx(5x)ln C(1+5x)D              ...(i)

Q: -3 -2 -i O Graph of f' The graph of f', the derivative of the function f, is shown above. On which…

A: We know that, Let f ' be the first derivative of function f that is differentiable on a given…

Q: f(x) = x(x - 9)2 (a) Make a sign diagram for the first derivative. f "(x) = 0 Vx E"x) = 0 F(x) = 0…

A: Here we will use product formula of derivative. d/dx ( uv) = u d/dx ( v) + v d/dx ( u)

Q: The derivative of cos²x - sin² x 01 sin x cos x sin² x - cos x sin² x sin x cos²x t² dt is cos x…

A: Given query is find the derivative.