Suppose f (x) =xsec(x²) tan(x²). )dx Evaluate: xsec(x²) + C B 2sec(x²) + C sec(x?) + C

Q: Find the derivative of f(x) =tan-1 (cos 6x) 6 sin 6x a. f'(x) = 1+cos? 6x - sin 6x b. f'(x) = 1+cos?…

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Q: Given g(x) = ln[(x^1/3 + sinx - 3tanx)/3x^4 - x^1/2], calculate g'(x)

A: Given equation is , gx=lnx13+sinx-3tanx3x4-x12 Let's find g'(x) Formulae we are using here,…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x +4 sin(a %3D If f(0) = 3 and f'(0)…

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Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: Consider the function f(x) whose second derivative is f''(x) = 8x + 6 sin(x). If f(0) = 2 and f'(0)…

A: Given  f''(x) = 8x+6 sin(x),  f(0)=2,  f'(0)=4 We have to find the value of f(3).

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: |2tan x In (cos x) dx=

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Q: Use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Consider the function f(x) whose second derivative is f"(x) = 3x + 8 sin(x). If f(0) = 2 and f'(0)…

A: Consider the second derivative function, f''x=3x+8sinx Given, f0=2  and f'0=2 We need to find f(x).…

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Consider the function f(x) whose second derivative is f"(x) = 6x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given,

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

Q: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)

A: We have to find derivative

Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 2 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

A: Given: 53.   fx=xlnx,  0,∞

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Consider the function f(x) whose second derivative is f''(x) 8x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given : f"(x) = 8x + 3 sinx, f(0) = 4, f'(0) = 4,    To find : f(5)?

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 4 sin(x). If f(0) = 4 and f'(0) =…

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Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: Find the 2nd derivatives

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 3 sin(x). If f(0) = 4 and f'(0)…

A: see the details solution in below

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 6 sin(x). If f(0) = 2 and f'(0) =…

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: f(x) = cos (In (3x))

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Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 3 sin(x). If f(0) = 3 and f'(0)…

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Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

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Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f" (x) = 9x + 3 sin(x). If f(0) = 3 and f' (0)…

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Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)

A: Find the derivative of function

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

A: Given function is f"(x) = 9x + 10sin(x)

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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