13 + 3z2 h(z) 3z2 g f' - f-g' g2 a) Use the Quotient Rule, %3D (Fill in each blank, then simplify.) h'(z) = 田).(1 !! !! %3D b) Use algebra first to simplify h, then differentiate without the Quotient Rule. h'(z) =

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A:

Q: Differential function of x2 + 2x + 3tanx

A: The given function is: x2+2x+3 tan x

Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: using at the y-cc

A: Given equation is: xy31+y2=85 Then we get, 5xy3=81+y2⇒5xy3=8+8y2⇒5xy3-8y2=8 Differentiating both…

Q: 11) Find the derivative of y = 3x (2æ² + 5x) Use two methods: Product Rule and Foil First method

A: Find the derivative of y

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A: Volume of the rectangular box= (Length)*(Breadth)*(Height)

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A:

Q: 16. Sinusoidal functions do not have any critical points.

A: False. Sinusoidal functions has critical points.

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A: You need to use reduction formula to integrate the function, such that: You need to use integration…

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A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

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A: We will find the integral as following.

Q: tion of all components of v(3) correct to two decimal places.

A:

Q: 3. U sin g Derivative Product rule 3. (x + 6) (x + 5); 4. 4x² (x – 1)

A:

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: In 2x -dp-

A: To evaluate the integral: ∫2ln2xxdx Solution: Let substitute t=ln2x. Differentiating both sides, we…

Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: 4 Test for homogeneity fx,y)- tanx- see'x - Osy

A:

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: 6. Use implicit differentiation to find first order partial derivatives: tan-(x²y) = y²z3 +…

A:

Q: 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative 10. y = -3 cot 2x, 2nd derivative

A: Question 8,Given,            y=-5e3x2To find : Determine the 2nd derivative of the given function.

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A: Given sinh(3-j5)3+j443-j52-j73-j7.  To evaluate the given expression.  The formula for…

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A: Indefinite integral is the process through which one can determine the function which on…

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Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

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A: We can find the answer as below.

Q: 7. y = 4 e2x, 4th derivative 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative

A:

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

A:

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

A:

Q: 6. Use the rules for derivatives (not the definition) to find the derivatives below. You do not nced…

A: Given: f(x)=y1=x-x2   and g(x)=y2=2x+12(1-2x) We have to find the derivative of the given function…

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A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

Q: x2 - 1 :) = x² + 2' refer this time? ag .2

A:

Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

A:

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

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Q: 6. DETAILS Verify the statement by showing that the derivative of the right side is equal to the…

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Q: sinh-1x = In (x + vx² + 1) %3D

A:

Q: prove that cosh^2x-sinh^2x=1

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

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A: Given information:

Q: sinz 3. а) Find the derivative of the function f(x)= [ (1-r²) dt using FTC-1. 3a. b) Verify the…

A: To find -  Find the derivative of the function fx = ∫cosxsinx1 - t2 dt using FTC-1. Verify the…

Q: Number 8

A: first find the derivative.

Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

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A: We have to find integration

Q: 3. f(x) = 6xi – 3x ; x € [- 2,1 first derivative critical numbers stationary points End Points…

A: Here, the given function is: f(x)=6x53-3x23; x∈-2,14

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A: Given,  A power function y=axp passes through the points 3,781 and 6,71296. The equation of power…

Q: 1- Genx :1 CSCX 2 CSCX=1 senx CSCX = I CSCX = 2 %3D 2- Cotx = 3 tanx= 3J3 3. 3 tanx = Cotx 3. 13 353…

A: first one is wrong.because secx=1/cosx.and sinx=1/cosec x.

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Q: J7 -dz 21-8

A:

Q: 3 8. y = sec Зx) 9sec (2 – 3x)tan´(2 – 3x) B. - 9sec (2 - 3x) tan tan (2 3 С. 9 sec' (2 — 3х) tan…

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Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step