Determine the function f satisfying the given conditions. f'(x) = -sin(x) f (7/3) %3D = 3.5 f (x) = A sin (x) cos (x) + D %3D A = B = C = D =

Q: Find  (f −1)'(a). f(x) = 3x3 + 3 sin x + 3 cos x,    a = 3

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Q: Differentiate the function. 8 + sin(t) f(t) cos(t) (a) f'(t) = Find f'(T). (b) f'(1) =

A: a:Here, f(t) =(8+sin(t))/cos(t)The derivative of f(t) is calculated as follows:

Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: Find f(t) given that f"(t)=sin(x) + cos(x) - 10, f'(0)=10, and f(0)=20.  Please show steps. Thanks.

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Q: Identify the function f (x). I (x) = (f (x))° = cos 2x

A: Given,          lx=fx6=cos62x

Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: Find f"(x) for the function f (x): = x cOS X

A: The given function is fx=xcosxTo find f''(x)

Q: f(x) = 10 sin x + 9 cos x f'(x) = %3D %D

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Q: 4x Let F be the function defined by F(x) = cos(t?) dt. Find an expression for 3. F'(x).

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Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

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Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Find the intercepts and points of inflection for function y = sin(x) - 1/18sin(3x) over the interval…

A: Given that y = sinx - (1/18) sin3x ;(0<=x<=2π). We find intercept point  and point of…

Q: Find the derivative y = √√x S 3t cos (16) dt 0 A. 3 cos (x³) -3√√x sin (x³) OB. 3√√x cos (x³) OC.…

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Q: Let f (x) = 4 tan (7x). Find the values of the coefficients in the expressions for f' (x) and f"(x)…

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Q: Find f′(x) and f′(c). Function f(x) = x cos x Value of c = /4

A: The given function f(x) - f(x) = x cosxDifferentiation on both sides with respect to 'x' to get the…

Q: Q.2: Find dx 2) | (cos²x sinx )dx

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Q: Find (f −1)'(a). f(x) = 4x3 + 5 sin x + 2 cos x,    a = 2   (f −1)'(a) =

A: Consider the function f(x) =4x3+5sinx+2cosx.Compute the derivative of the given function as follows

Q: 3. (a) Determine whether the function y=1-cosx is even, odd or neither. (b)Find antiderivative of 3…

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Q: Let f (x) = 2 tan (5x). Find the values of the coefficients in the expressions for f'(x) and f " (x)…

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Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

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