Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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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: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: sin 3t dt J cos 3t – 1

A: Given: I=∫sin3tcos3t-1dt   ....(1)   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where…

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: Can i get help step by step please

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Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: Find a differential equation that corresponds to the given direction field.

A: This is a problem of slope field.

Q: 5 sin“(3t) dt

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: Calculate the derivative 23 d dz using Part 2 of the Fundamental Theorem of Calculus. 23 dt = dz -1

A: ddx∫-1x6t5-t23dt = ?

Q: 15 dy dt 2-

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Q: 5. x- + Px = sin t %3D dt

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Q: 33 2Vx- f(x) = T sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x (1–3t)5(t³-8) alt) t # 2

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Q: 5

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Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 0. y = 3…

A: Given, y=∫ex03 sin2(t)dt  We need to calculate the value of y' It is of the form of…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (The…

A: Solution :-

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: tan st e dt 2

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

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Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

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Q: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

Q: Can i get help step by step please

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Q: Compute the derivative.log(sin(t))

A: Given: ddtlog3sint To find: We have to find the given derivative.  Required formulas: logab=lnalnb…

Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.  g(x)=…

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Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: Use the Derivative Rule in Section 3.8, Theorem 3, to derive d 1 sec dx x. 지 V - 1 1지 > 1.

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Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

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Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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

A: Given: y=∫x22x2lnt dt

Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h (x) =…

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: Can i get help step by step please

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