x3 +x2 3 Prove that if f (x) then f"(x) = – x² Find g'(x) and g"(x) if g(x) = (2x – 3)² (x + 4)³. 2 - Va 2+ Va Find f'(x) and f" (x) if f(x) %3D

Q: Given that f(x) = V h(x) = x³ g(x) = = %3! Find (f ogo h)(x)

A: Composite functions concept is used.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: 4x2 + 3x + 2 If f(z) = then: f'(z) - f'(3) -

A:

Q: Find df/ dx of  f(x)=(x2-1)(x3+3x2/x2+2)

A:

Q: 1 Po(x) = v2 3 P1(1) = : %3D "V 2 PĄ(2) = (3=² – 1) V P3(x) = ; (5x³ – 3r) /5 Write down the…

A: We will find out the required values.

Q: Let f(x): = Compute f(x) f'(x) = f"(x) = = 4 + 6x x

A: given function is  f(x)=4+6xx=4x+6 then computing following :----   f'(x)=ddx4x+6=-4x2…

Q: nd and simplify 2² x² (f(x) g(x)). O d² O −(ƒ (x) g(x)) = ƒ” (x) g(x)+ f (x) g″ (x) Hint 2² -(f(x)…

A: Given query is to find the double derivative.

Q: 3. When is the function increasing and when is it decreasing? f(z) = re==z3)? xe 2 f(x)=xe 4X2)

A: Solution:

Q: Find a function f(x) such that ƒ'(x) f(x) = – 6x² – 1 and ƒ(0) = 5

A:

Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

A:

Q: Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the…

A: F′(x)=(x+2)22​Explanation:If you have any questions let me know in comment box thankyou for your…

Q: f(x) = In(5 + 4x)

A: Given: - The function is, f(x)=ln(5+4x) To find: - The derivative of the given function.

Q: C Chain Rule 7) f (x )> (2x +5)

A: To determine the derivative using chain rule.

Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

A:

Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

A:

Q: Yob) a) fog)(x) & 3. = (x)) JI 2. x+2 (x)6 8 %3D then find

A:

Q: Let ƒ(x) = (7x² − 7)¹ (6x² − 3)⁹ - Find f'(x) = do not oxpand an

A:

Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

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Q: f(x) = In (1+x³)

A:

Q: lo UcE - Uxx=0 4(x,0) = f(x) 4= (x2,0) = g(x)

A:

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

A: We have to find the interval in which f(x) and g(x) are decreasing.