We have f(x): f(x) = {sin2x 0 >ܝ TT 2

Q: If g(t) = (√t 4) (√t + 1), then: g'(4) =

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Q: 8. Find the function Sthat satisfies the given conditions. )S"(=) = sin r – e-2" with S"(0) = } and…

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Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find ƒ'(1). f(1) = 10 X Type here to search

A: I am attaching image so that you understand each and every step.

Q: Apply the special case of the general power rule d/dx [h(x)]2 = 2h(x)h(x) and the identity fg =…

A: dhx2dx=2hx·h'x  &  fg=14f+g2-f-g2

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: tan x If f(x) = 3 sec a f (2) = f (1) =

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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 =

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Q: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: (3x3+3x-5x2) 1- is x2 e0.5x2 xp e-2x2 3- S sec'x? tanx² xdx xp 4-(Csc Vx cotvF xp

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Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: Ql:- Find the domain of the following functions a) S(x) = sin"*(2 – 3x) b) f(x) = sec"*(x – 2)

A: we have to find domain

Q: how

A: Que seems some data missing. Though I have simplified the given expression as much as possible.…

Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

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Q: lim

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Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

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Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

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Q: Determine f(x) a. f(x) = 4 sin² (x - 2) b. f(x) = 2(cos x)(sec² x)

A: (a) The given function is f(x)=4sin2x-2 Find the first derivative…

Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

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Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: Find f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

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Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

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Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

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Q: 3 Find f such that f'(x) = - √x f(x) = f(1) = 12.

A: Solve for the f(x)