a. Σχy, i=1 b. Σ(x)(y) C. (Σ' (Σ'

Q: 10. (a) State the Fundamental Theorem of Calculus. -x sin t %3D (b) Let J(x) = S*. Evaluate: (i)…

A: Fundamental theorem of calculus

Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

A:

Q: If a(x) = 2 – 8x, what is an equation for a (x)? O A. a-1(x) 2. 8. O B. a '(x) = ?= 2 8 al(z) = ", 으…

A: The given equation for a(x) is: a(x)=2-8x

Q: Verify the following properties for ƒ(x) = sin x and p3(x) = x - x3/6:                    ƒ(0) =…

A: We first find the derivatives

Q: h(y) = et. In (g) Find b'(a)

A: Topic:- calculus

Q: Use implicit differentiation to find an equation of the tangent line to the graph at the given…

A: As per the guideline, I am supposed to solve only first question from the given problems.

Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: Find g'(π/4).

A: Given:

Q: If y = xsin then y is equal to = X" at x =

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Q: Let h(t) = tan(3t + 8). Then h'(5) is and h"(5) is

A: As we know that the chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1   Given: ht=tan3t+8 Now…

Q: For cos2(xy) =, evaluate y' when x = 4

A: Given that: cos2(xy)=14

Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

A:

Q: Let F(x) = f(x°) and G(x) = (f(x))* . You also know that a° = 14, f(a) = 2, f'(a) = 3, f'(a") = 6…

A:

Q: 1 If f(t) cos(6t), find f'(t). Use exact values. f'(t) =

A:

Q: (tanx) y' = y, y(플) = 플 T

A: Given differential equation:- tanxy'=y

Q: . Consider f(x) = 4 - x2 , g(x) = Vx + 3, h(x) =. Evaluate the following. %3D 1. (f° g)(1) 2. (g•…

A: Explanation of the answer is as follows

Q: Let f(x) = t° dt. Evaluate the following. f'(x) = f'(5)

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Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: Find y as a function of t if y(0) = 8, y'(0) = 4. y(t) = 6y" + 33y = 0,

A:

Q: 2. Given f(x,y)=xy°e*: (a) Find the first derivative f,(x,y). (b) Find the first derivative f,(x,y).…

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Q: If xy + e' = e, find the value of y" at the point where x = 0.

A:

Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

A:

Q: 4. Let f(x)= 5Vx and g(x)= 4 + sin x. (a) Find (f ° (x) and (f ° g'(x). (b) Find (g ºf)(x) and…

A:

Q: Let f(x) = x°e*. Find f '(x).

A: Product rule:d(uv)dx=udvdx+vdudx

Q: If f(y) = tan- (3y*), find f' (y). Use exact values. %3D f'(y) =

A:

Q: 6. Find y' in each case. Do not simplify your answer. 2 tan x C) y = VI – x² - d) xªy + 5y®x³ = 8.…

A: