If y = f (x) = In (cosx), then, f' (x) =? O tan (x) O-sinx (x) -tan (x) O-cot (x)

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A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

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Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

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A: derivative

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A: Given that: ∫sinhx.coshx.dx

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A: As the function involved function in a function we can apply chain rule and find the derivative of…

Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: What do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

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Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

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A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

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: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

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Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

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Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: Find integration + dx Cos (x-1)

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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: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1.

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: 3- - 플 플 sin²cyl y จน

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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: sinx In (2) co cos x

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Q: Find the first derivative of the following function: 1. y = sin (2x) - cos (2x)

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Q: Find cosh æ In(sinh x)dx.

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Q: 1 3), sinh(x)-cosh(x) dx

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Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

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Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

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A: we are given the function is  f(x)=1+sin2x2cos3x

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A: Given: 8cosxy+x4=y4 For finding derivative of given expression, we differentiate given expression…

Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

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Q: 3 cos x Evaluate | dx by using substit ution method. (1+sin x)“

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Q: |sin x.cos x %3D 1+ 2.ln x

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A: Sum/difference rule of differentiation,

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Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…

Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Q: Compute f sin(cos(x²)) sin(x²)x dx

A: