5. If f:1 → R is differentiable on I and f(x) 0 ,f'(x) ± 0 for x € l if g(y) =÷ , y# 0 what is (gof)' by usin y chain Ruie mathematical analysis

Q: 20. Sketch the function with the following properties: f'(x) 0 on (-2,0) f"(x) 0 on (-co, -1)…

A: From the given information, following results can be deduced.

Q: 1. Let f, g : R" → R and let 9(t) = f(t, x2, ..., an) and (t) = g(t, x2, ., Tn) where x2, .., Tn are…

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Q: 2. Let u,v be functions of x. The first order derivative of uv can be derived by the following…

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Q: 11. (b) On the axes labeled (b), sketch the graph of the antiderivative F off satisfying F(0) = 0.…

A: We have to graph the following function f.

Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: 2 (y – k) y' = 4a Find the Derivative - d/dy Since 4a is constant with respect to y, the derivative…

A: (1). The given expression is:2y-ky'=4a

Q: Let f and g be differentiable functions such that f'(0) = 3 and g' (0) = 7. If h(x) = 3f(x) - 2g(x)…

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Q: What is the derivative of y = 3x²tan-1(x)?

A: ddxxn=n xn-1ddxtan-1x=11+x2 One have to use product rule here, which is ddx(uv)=vddxu+uddxv

Q: d g(s) be two differentiable functions in R and f  (2) = 8, g(2) =0, f(4) = 10 , and g(4) = 8 Then…

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Q: 36. Let f be a twice-differentiable function of z such that, when z = c, f is increasing, concave…

A: We have given function of x which is twice-differentiable such that when x=c, f is increasing,…

Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: 23. The graph of a differentiable function ƒ is shown. If h(x) = f(t) dt, which of the following is…

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Q: Prove tht the fallowing ralt U(1-k)-2U(t) + U(t + k) U" (t) =- with an enor of ortler k?, which is…

A: The objective is to prove the central difference approximation to the second derivative of Ut…

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: A cylindrical vessel without lid is 4 cm in radius and 10 cm in height. If the vessel is to be…

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Q: Suppose g and h are everywhere differentiable functions such that g(2) = 1, g' (2) = 2, h(2) h'(2) =…

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Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

Q: The function f is contin'ous function with the the intervel fo,-3) u(3,00 the interel (3,-) U (-1,3)…

A: Charaterstics: If f'(x) &lt; 0 ; function decreases                 ; x∈-∞,-3 ∪3,∞If f'x = 0 ; no…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: Let z be a differentiable function of x and y related by the following equation: x+z (√y + cosh(z))…

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Q: In calculus, the derivative of f (x) is denoted by f '(x), andthe value of the derivative at x = a…

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Q: What is the first-order derivative of y = x^y?

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Q: . The derivative of w = f(z) at z = zo is given by f(zo+Az)-f(zo) Az f'(zo) = lim Az→0 = lim = Oz+z…

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