Theorem: The Chain Rule provided If m(x) = EI(x) is a composite function, then that E'[I(x)) and I'(a) exist.

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

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Q: Let H(x) = F(G(x)) and J(x) = F(x)/G(x). Suppose F(4) = 9, F'(4) = -7 G(4) = 3, G'(4) = 0 G(-6) = 4,…

A: Given H(x)=F(G(x))H'(x)=G'(x)*F'(G(x))J(x)=F(x)G(x)J'(x)=G(x)F'(x)-F(x)G'(x)G2(x)

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: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Sketch a graph of a function f(x) that satisfies all of the following. f(-3) = -3, f(-1) = 2, f(2) =…

A: Graph of function using given information

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Sketch a graph of a function f(x) that satisfies all of the following. f(-3) = -3, f(-1) = 2, f(2) =…

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Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

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Q: Let h(x) = f(g(x)). If: f(3) = 0, f'(42) = –5, f'(3) = 4, g(3) = 42, & gʻ (3) = 0, then h'(3) =

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Q: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

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Q: or h' (x):

A: Given that: The equation is h ( x) = g ( x 2 + f ( 3x) ).

Q: If f and g are functions such that m(x) = f(g(x)), g(3) = -4, and g'(3) = 10, what additional…

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Q: f(x)+h(x)=g(x) what is g'(x)?

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Q: If m(x) = E[I(x)] is a composite function, then and I'(x) exist. O m'(x) = E[I(x)]I'(x) ○ m' (x) =…

A: Stepwise explanation is given below Explanation:

Q: f(x) = ex/³; [1₁3]

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). (a)…

A: u(x) = f(x) g(x)u'(x) = f'(x) g(x) +f(x) g'(x)a) u'(1) = f'(1) g(1) +f(1)g'(1)from graph f(1) = 2 ,…

Q: Differentiate the function. fx) = (4 +x*)° - (1+x*) %3D f'(X) =

A: We have to find derivative

Q: = (F(x)). Let F(x) = f(f(x)) and G(x) You also know that f(3) = 12, f(12) = 3, f'(12) = 7, f'(3) =…

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Q: Let g(x) = = X-f(x) S(x) , find g'(1),if f(1) = 4 and f'(1) = 2

A: Given that g(x) = -x-f(x)f(x). We have to find the value of g'(1). Given that f(1) =4 and f'(1) =2.…

Q: Prove that if f(x)=c (a constant function), then f'(x)= 0

A: Given query is to prove that derivative of constant function is zero.

Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: uppose that f and g are functions such that f(5)=3, f'(5)=-2, g(5)=4, and g'(5)=-5. nd h'(5) where h…

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Q: Differentiating the function f(x), using the Chain Rule. f(x) = {Vx5 + 6x f'(x) = =(x5 + 6x) 3 A 5x4…

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