R² and r are defined by SR E(*; – T)(yi – ỹ) Say R? SST' r = VE(x; – #)² L(yi – g)² (1) Show R² = p2. (2) Define \ as E(yi – 9)(ŷ; – ) - - Show X² = R². (Note that ĝ = ŷ)

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

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Q: 1) y = logs Vr² – 1

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

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

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A: Given: cos10x=sec50y To Find: if y'=10sin10xgythen gy is equivalent to: Concept: i. ddxcosx=-sinxii.…

Q: All Sections 1) Solve the following equations for t Jy evt = 2) Find the derivative of y with…

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Q: If gw + xcos tgcx) = x7, find gro) g'co) =

A: We have to find

Q: Let (t) = Find '(t) '(t)=<

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Q: prove the following relationships. Note that x(z) = ] [x(+)]. 1. ] [ a^² XLE)] = x ( ² / ) 2. ] […

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Q: 8. 9. 10. Given f(x) = cos(3x + π), find ƒ'(π) a) 0 b) -1 c) -3 If f(x) = √ex, the derivative is: a)…

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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: 2. Suppose f(x+3)%3D f(xr), what is the period of the function f ? (A) 4 (B) 3 (C) 2 (D) 1

A: topic - functions

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: Let h(x) tan(5x + 7). Then %3D h'(4) is and h''(4) is

A: As in question it is not mentioned wheather we have to considered degree or in radian inside…

Q: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

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Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: dy 1- Which one is correct ? The Y of ex?tanx a) (x2 sec?x tanx + 2x tanx) b) (x² sec?x + 2x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted…

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Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

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Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Determine r (x) if r(x) = (arccot(x))".

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Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

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Q: Consider the table of vales for the functions r). J ), u() and g'(x): If the function k is defined…

A: Given, k(x) = f(g(x))

Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.