f"(x) = cosx – tan x. f'(x) If f(x)=enx, show that = cos x-

Q: IT Evaluate the integral: (cos x + sinx cosx)dx

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Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: (5x) S sin(x) tan(x) .........

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Q: determine the general derivatives f(x)= -3 f(x)= sin x + cos x -sec2x

A: Simple use the identity of derivative of constant is zero and derivative of sinx is cosx and…

Q: If x = ln ( sec x + tan x) , show that sec x = cosh x

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Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

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

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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: Find the first derivative of y = x (cos(In x) = sin(Inx)) O-2 sin(In x) O sin(In x) O 2 sin (In x) O…

A: derivative

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

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Q: Compute the derivative. f(x) = (cos2 x)cosx

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Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

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

Q: Integrate: S tan (æ) sec³(x)dx

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

A: here we have to integrate the given integral.

Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

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: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: compute the derivative.  f (x) = (cos2 x)cos x

A: To compute the derivative.  f (x) = (cos2 x)cos x

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

A: Find the derivative

Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

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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)

Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

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

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Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

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

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Q: Find the derivatives of the functions in Exercis

A: fθ=sinθ1+cosθ2

Q: Is it true that the derivative of y=arcsin(cos2x) is -2?

A: The function is y=arcsincos2x.   Differentiate the function with respect to x.…

Q: Find first and 2nd derivative guncic 2 tan2x 3.

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

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

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Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: Find the derivative 1. h(x) = cos3(tan2x) 2. h(x) = x5 sec(1/x)

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Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)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: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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

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

Q: /1 – ť dt dx cos X

A: This is a basic calculus question

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Use Leibniz’s Rule to find the derivatives of the functions

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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