1 (1) u(x) = x + f * u(t)dt, u(x) = x+ 24 2 (2) u(x) = ² = x + √² xtu(t)dt, u(x) = x (3) u(x) = x + [xtu²(t)dt, u(x) = 2x

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: If f(x) = 1+/x, then f'(x) = -1 A 4/xV1+/x 1 B 4V1+x 1 4/x/1+Jx 1

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Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

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Q: Show that 1 < arg (z).

A: Inequality - A statement of an order relationship—greater than, greater than or equal to, less…

Q: f(x, y) = V 2 2 3x² + 4y²

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Q: function of xx if

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Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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Q: (x²ex²+y ) f(x,y) = } 7²+y2 , (x, y) # (0,0) 0, (x, y) = (0,0) Calculate fx (0,0) or show why it…

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Q: Show that fy(y) = n[1-Fx(y)]™1 fx(y)

A: Please see that slight information is needed here. which is to be mentioned that    X1, X2,......,…

Q: Find the derivative of y=x√x + 1. 1 dy = 2(x+1) ³ + √² ž √x+1 dy dx = dy dx dy √x+1+ dx = x √x+1 = =…

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Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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