Differentiate the following functions with respect to x (i) f(x) = sin² Vx² + 1 In(x²-3x) sec(7-3x2) (ii) f(x) =

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: Evaluate the first derivative of the following functions: g(x) : = cosx – sinx f (x) = 4x²cosx g(y)…

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Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = 1/8 is approximated by the…

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Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?

A: Verify the result by implicit differentiation as follows.

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: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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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: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

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Q: Find the derivative of y with respect to x. y = 2x 4 sin -1 x

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Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

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: Find the derivative of the function. f(x) = V4 +x sin x 4+x sin x = dx

A: Derivative of the function is given below

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 second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For…

A: Differentiate two times

Q: Find the derivative with respect to the independent variable. f(x) = 9 cos x - 2 sin x f'(x) = D %3D

A: We have to find derivatives of function: fx=9cosx-2sinx We know the derivatives of trigonometric…

Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

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: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: Find the second derivative of the function. f(x) = sin(2x?) %3D f "(x) = 16x sin 2x) + 4 cos 22)

A: Given f(x)=sin(2x2) Formula: Derivative of sinx  = cosx Derivative of cosx = -sinx

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: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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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 derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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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: 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: Compute the derivative f'(x)given sin x 1 dt 1- 12 f(x) = cos x

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Consider the function f(x) whose second derivative is f''(x) = 5x + 7 sin(x). If f(0) = 2 and f'(0)…

A: Given :f''(x)=5x+7sin(x)

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+v3 3' 2v3 At the…

A: Given: f(x) = 1 + csc(x) -cos(x)   To determine: Equation  of the tangent line at the point…

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

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Q: Find the derivative and simplify A. f(x) = 2 sin−1(4x + 5) B. f(x) = x3tan−1(x2)

A: Given:- A.   f(x) = 2 sin-1 (4x + 5)   B.    f(x) = x3 tan-1 (x2)  To find :- Derivative of given…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Given, f''(x)=10x+8sinx(x) After integrating the above equation,…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinaxdx=-cos(ax)a+c ∫cosax dx=sin(ax)a+c ; where 'c' is an integration…

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

A: Find the derivative of function

Q: Use the definition of a derivative to find f' (0) where: x² sin() x + 0 f(x) = x = 0 If the…

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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: Find the inflection points for the function f (x) = 8x + 2 – sin (x) with 0<x< 3T. Express the…

A: The given function f(x)=8x+2-sin(x)

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

A: We need to find f(5).