If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) h(1) = 5 h'(1) = -7 g(1) = 4 g'(1) = 1 fx(4, 5) = -5 fy(4, 5) = 6 find dz/dt when t = 1. dz dt =

Q: 2x If f is the function given by f(x) = Vi? -t dt , then f'(2) =

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Q: Let 3 4 f(x) = (x° + 5x + 8)* f'(x) = f'(3) =

A: Chain Rule

Q: · Sº t³ dt then f'(x)= If f(x) = and f'(-2) =

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Q: If f(x) = t* dt then f'(x) = f'(4) =

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Q: f(T) is a twice differentiable function with f(0) = 5, f(1) = 4, f'(1) = 2, Then Calo

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Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: If f(x,y) = ln(xy) + x2y2, in what directions is the second directional derivative of f(1,1) = 3?

A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

Q: 3 (b) * ƒ (x) da 0 =

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Q: 2z If f(x) = , V1+t° dt, then f'(x) : = 1 Select one: a. -2x/1-8r3 ****** b. -2x/1+ x C. -2/1 – 8x O…

A: Recall the Leibniz rule:

Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: F:[- 2, 2]→ R, F(x) = (- 3Xf + 1) di

A: Given: Fx=∫-2x2t-3t2+1dt For finding derivative of given function, we will use fundamental theorem…

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: 14 If f(x) : t? dt then f'(x) =

A:

Q: 15 [ = f(x) = H t²dt then

A: f(x)=∫x15t2dt

Q: (x) = ₁² ² sin(t) -4x 1+t2 If f(x) = -dt, then f'(x) =

A:

Q: Q3. Find the indicated derivative(s). (a) g(), where g(1) = f(x(1), y(1)), f(x, y) = x²y – sin y,…

A: Note the below results : Suppose gt=fx,y where x=xt and  y=yt .Then according to chain rule…

Q: If f(x) - Sto = t5 dt then f'(x) = and ƒ'(−4) =

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Q: . If F(x)=√√√4t² + 1 dt, find F(2), F'(2), and F"(2).

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Q: = [² If f(x) = then f(x) f'(x)= f'(-2) = -1 to dt

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Q: 49. Differentiate y = cosh²4x a. 4(sinh 8x) b. 12(sinh 8x) c. 8(sinh 8x) d. 2(sinh 4x)

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Q: 16. Consider F(x) = dt. Find F"(x). 1 2 1 (A) I+8x (B) 1+2x (C) 1+ 8x (D) 1+8x

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Q: Suppose f = f(g, h), g = g(t), and h = h(t). Find df/dt when t = 2, given the following. g(2) = -9,…

A: We have to find value of df/dt at t=2

Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: If f(x) x = [²₁ 1 = = then ƒ'(x) = ƒ'(−2) = tadt

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Q: If f(x) t2 dt then f' (x) = f'(3) =

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