(4) Suppose z = f(x, y) where f is differentiable (both f, and fy exist). In addition, suppose = g(t) and y=h(t), and I= dz Find when t-3. dt g(3) = 2, g'(3) = 5, fr(2,7)=6, h(3) = 7, h'(3) = −4, fy(2, 7) = −8.

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

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: Let f(x) = V9 + v7z. Find f'(x) f'(x) =U

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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: If f(2) = 1, f'(2) = 2, g(2) = 2 and g' (2) = 1, then f(x) g(z) %3D %3D %3D

A: Given : f2=1f'2=2g2=2g'2=1

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

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Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: 3. Find the derivatives of the following funct a y = sin z?, y" b. h(2) = (9z + 4)š, h(3)(z) c.…

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Q: A function h(x) = = Compute h'(3) if x-2 f(x) f'(3) = 2 and f(3) = 1. is defined in terms of…

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Q: 3 (b) * ƒ (x) da 0 =

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Q: r(x)=f(g(h(x)))，h(1)=2, g(2)=3 h'(1)=4, g'(2)=5, f'(3)=6, r'(1)=?

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Q: Let H(x) = f(xg(x)), where f and g are differentiable functions such that g(2) = 3, g' (2) = 5, and…

A: We will solve the following.

Q: Evaluate f'(x) at x =2 given f(x)= (x²– 3)“

A: The given function is fx=14x2-34. Evaluate the differential of function at x=2.

Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

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Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: 3) f(t) = t*e?t %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Given that f'(x) = Vz +6 and g(z) = r² – 3, find F'(z) if F(r) = f(g(x)). F"(2) -O

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Q: Let F(u, v) be a function of two variables. Let F,(u, v) = G(u, v), and F,(u, v) = H(u, v). Find f'…

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Q: ii) Let F(x) = f(rf(xf(x))) where f(1) = 2, f(2) = 3, f'(1) = 4, f'(2) = 5, and f'(3) = 6. Calculate…

A: Given function is F(x)=f(xf(xf(x)))