Question 1 Let f(x) = x + √x. Find f'(1) at x = 1. A) 0 B) 1+ 2√ C) y = + ³/ D) 1/ E) /

Q: Differentiate the following function: f' (t) = f(t) = √t – .

A: f(t)=t6-1t6d dt(tn)=ntn-1we know ba=(b)1a

Q: f(x) COSX f'x) 2.

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Q: Find f. f(x) = 3 f'(x) = √√√x³ + ³√√x + 5ex + sec² x, f(0) = 8 4

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Q: Question 5 x3+5 Determine f '(x). f (x) = (A 1- 10x-3 B 3x2 3 2 (D 5x4 + 10x 2.

A: Given: fx=x3+52   As we know that; The sum./difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: Find f. f ''(t) = 12/sqrt(t)                          ,    f(4) = 38,    f '(4) = 18   Recall that…

A: Given Integrating both sides, we get But f'(4)=18

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: ) FIND F'6): c. f() - x 2- 3x2 F. f6) = VI-x

A: f(x)=x2-3x2differentiate w.r.t.…

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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Q: Find f. f(t) = f'(t) sec(t) (sec(t) + tan(t)), -2-√2 x Need Help? Read It Watch It - 1/2 < t < 1/₁ (…

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Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: Q6. Verify that 8²1 əxəy for the function f(x,y) = ln(2x + 3y)

A: Given,            fx,y=ln2x+3yTo find : Verify that ∂f∂x∂y for the given function.

Q: Differentiate the functions. a) f(x) = 2 – 3x + b) f(x) %3D Зе* + sinx c) f(x) = 3x

A: As per guidelines, we will solve only first three subparts. Kindly repost other subparts separately.

Q: Question 7 Find f(x), when f'(x) = xe and f(0) = 1. A) ²e²² +1 B) re +1 C) 1 D) ez² +2x²e²² E) /e² +…

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Q: Let f (t) = et sin 7t Part (a) Find L{f (t)} Part (b) Find L{f' (t)}

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Q: If sinh(æ) = -4 , then coth(x) = (A) (B) =VI7 (C) =VE V15 (D) 4 15 (E) E O (A) O (B) o (c) O (D) O…

A: Solution

Q: Find ao of the function f(x) = ÷(n - x)² |3D IT ^ 2/12 O 5 T^ 2/6 π^ 2/6 O T^ 2/6 5 π^ 2/12

A: Fourier coefficient ao of the function in the Fourier series

Q: Given f''(x) = 3x – 6 and f'(– 3) = – 2 and f( – 3) = - 1. Find f'(x) = and find f(4) =

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Q: Differentiate f (x) = (cos 3x)V* %3D

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