c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3 h(x) 4 2 0 4 2 0 02 3 1

Q: If f (0) = 3, f'(0) = –1, g(0) = –2, and g'(0) = 5, find h' (0) (a) h(x) = 2f(x) – 3g(x) (b) h(x) =…

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Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

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Q: If g(2) = 3 and g'(2) = 1 and f(x) = [g(x)]°, find f'(2) %3D

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Q: Find the equation of the tangent line to the curve f(x) = - -x4 at x = 1. O T(x) = 1 + (-4)(x - 1) O…

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Q: f(x) f (x) a (x) g' (x) 1 0 -4 -3 -2 2 -4 -3 -3 3 -4 4 5 14 4 6. 17 27 31 h(x) = xf(x)+g(2x – 5)…

A: to find h'(3)

Q: (3) The derivative of y = In √√x is (A) y' = √³ 2 (B) y' == / 1 (C) y' = 2√/x (D) y' = = 1/2 2x (E)…

A: As we know that, The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And use the common…

Q: 13. f(x) = (x³ - Зx)(2x? + Зх + 5)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (c) Let h(x) = . Find h'(1). f (x) (d) Let h(x) =2f(x)+g² (x). Find h'(4).

A: c.

Q: 5. Suppose f(3) = -2, g(3) = 5, h(3) = –1, f'(3) = -4, g'(3) = 3, and h'(3) 2. Find the value of the…

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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: 6- y = f(x) 5. 4 3. y = g %3D 2)

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Q: x2 - 4x - 12 Find f'(x), f'"(x), and f8(x) for the function f(x) X+2 f'(x) = everywhere that f(x) is…

A: Given

Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

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Q: If f(x) = f (x) „sin(x) e Then f'(0) = ?

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Q: f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1,…

A: Given : hx = fgxpx = fx·gxqx = fxgx

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f '(1) =

A: Given:  f(x) + x2 [f(x)]3 = 10 and f(1) = 2

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: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: If f (x) = e2" (x³+1), then f' (1) =

A: The function is given by fx = e2xx3+1 To evaluate : The value of f'(1)

Q: If h(x) = f²(x) – g°(x), f' (x) = -g(x) and g'(x) = f(x), then h'(x) is:

A:

Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

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Q: Find f'(2) for f(x) 2 (x-)-

A: Given; f(x)=(x-1/x)^2 We have to find f'(2)=?

Q: If f(x) = = f'(x) = f"(x) = 4x 5x2 +7 compute the first and second derivatives of f(x).

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Q: Find h' (2) given h (x) = ƒ (x) g (x and given -3, f' (2) = 5, and gʻ (2) = 1 f (2) = 3, g (2)

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Q: Suppose H(x) = f(g(x)) and %3D f(14) = 3 f' (2) = 13 g(14) = 2 d (14) = 4 Find H' (14)

A: Chain rule of differentiation:

Q: If f(x) = x+2/ 1-x then  f'(x) = ?

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Q: f(3) = X f'(2) = 2 3 f(x) -1 f'(x) 7 g(x) Given that f(x) and g(x) are differentiable and that…

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Q: Given F(2) = 1, F' (2) = 5, F(4) = 3, F' (4) = 7 and G(4) = 2, G' (4) = 6, G(3) = 4, G' (3) = 9,…

A: Given: F(2)=1, F'(2)=5,F(4)=3, F'(4)=7 and G(4)=2, G'(4)=6, G(3)=4, G'(3)=9 To find a)  H(4) if…