/is [sec2(x) – csc²(x)]dx Evaluate:

Q: Let y=sin2x. Differentiate this function without using the chain rule.

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Q: Integrate sin^2(7x)-cos(x)

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Q: sec 3x tan² 3x dx

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Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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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: Use integration by parts to verify the reduction formula.

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Q: Find fi( using the derivative rules tanx y2-3

A: Given, the function is                         We have to find the derivative of this function i.e.…

Q: Use the Power Rule to compute the derivative: %3D lx=7

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Q: df Use derivative rules to compute where f(x) = -2xe". dx x%3DIn 7

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

A: Given: 53.   fx=xlnx,  0,∞

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

A: I have stated the used formulas in the solution

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

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

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: x2 f (x) = t² sin(2t) dt 1

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Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: what is the implicit differentiation of: ysin2x=xcos2y

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Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

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Q: tan °(ln z) sec® (In z) Evaluate dz.

A: Evaluate: ∫tan3lnxsec6lnxxdx

Q: Find the derivative of f(x) = (1 + 7x2)(x − x2) in two ways. 1. Product Rule 2.Perform the…

A: For product rule we use u=1+7x^2 and v=x-x^2Product rule = u'v+uv'Answer: f'(x)=1-2x+21x^2-28x^3

Q: evaluate fsin.x dx inx dx JT+sin x A secx- tanx - x +C B secx + tanx +x+C C) secx + tanx - x + C

A: Here we have to evaluate, I=∫sinx1+sinxdx

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Verify the differentiation formula.

A: Given Data The differentiation formula is .   The formula of sech x is, The left-hand side of the…

Q: 1. у %3D 4x2 — 3х — 2.

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Q: adient of f in diro

A: Given function is: f(x,y,z) = xy + yz2 + xz3.

Q: What are the indeterminate forms and L'hospital's rule in application of derivatives?

A: We have to define Indeterminate form and L'Hospital Rule

Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: у %3DIn(In sec x)

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Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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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: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

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Q: 1. gx-) = - โ -เ sin 2x X< L2x

A: Given: gx-π=0x&lt;π12sin2xx≥π To find: Solution

Q: Q/Evaluate Integral:- sec2 3x dx tan23x-3 tan3x+2

A: To evaluate the integral:

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: Integrate (tanx)^3(secx)^3

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Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: /1 – ť dt dx cos X

A: This is a basic calculus question

Q: s(w) = In( w - %3D

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Q: Find the derivative using the First Fundamental Theorem of Calculus. 13)음 V8t +7 dt dx

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Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

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Q: 4 Find the derivative of f(x) using first principle %3D 3x2-3 of differentiation.

A: