5. If f (x) = (x + 1)(x2 – 2)3 then f'(x) da व्य 2= 2x (1) 2 A. & 6xx2 – 2)2 انی + (22 21 2 = Alv 3x + 1) (x2 – 2)2 aa 1 B. 6x(x( + 1)(x2 – 2)2 f" ( x ) = (x D. (x2 – 2)2(7x2 + 6x – 2) -

Q: If f(x) = (x6 + 4x) ³, then df(x) a) 3(x64x)² (x5 + 4) b) 3(x6 +4x)² Oc) (x6 +4x)² (6x5) da equals…

A:

Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

A:

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

A:

Q: Differentiate 3x-1 2x + 3 with respect to 'x'.

A:

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: If ƒ(x) = 3x√x + ƒ'(9) = x²√x then ←

A: f(x)=3xx+2x2xwe know  ax×ay=ax+yd dx(xn)nxn-1

Q: Find y" from x =t +7, y = 6t -1

A: Answer and explanation is given below

Q: 6) L (x- 3)(x + 2)? dx

A:

Q: d (tan² (2x³)). dx (a) 202¹ tan (2x5) sec² (2x5) (b) 20x¹ tan (25) 16. Calculate (c) 2 tan (2x5) (d)…

A:

Q: f(x) = Ax , g(x) = Bx^2 Find A and B if (f o g) (1) = 11

A: This is a simple question based on composition of functions which could be solved with the basic…

Q: The derivative of flx)= - 3x -2x? is 5+ 4x

A: Given that -      fx=3x-2x25+4x     f'x=?

Q: f(x) = C

A: Here we apply quotient rule of differentiation given as ddxuv =vdudx-udvdxv²

Q: 10) Find (ƒ^¯') (-5) if ƒ(x)= x³ +3x−1.

A:

Q: 1. f(x² − 3x + 7) + (2x − 3) dx

A: In this question, we need to integrate the given function.

Q: Let f(x) = x²+ Ax + B. By knowing that f(1) = 5 and f'(1) = 5, find the values for A and B.

A:

Q: If (2,9)=, then f„- If f(x,y)

A:

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

A:

Q: 4x - 7x Differentiate with respect to 'x' 6x + 5

A:

Q: e) k(x) = (2x-1) ³x

A:

Q: 9. f 6 sec¹ xdx

A:

Q: Let f(x)= ax'+x² + bx +6 where a and b are real numbers, and f(2)=3. Find the value of f(-2).

A: f(-2) = 17  The detailed solution is as follows below:

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

A:

Q: Simplify (2u + v) x (2u - v)

A: The cross product of a and b is represented by the expression, a×b=a b sin θ n. Where θ is an angle…

Q: K Find an equation of the line in the form ax + by=c, where a, b, and c are integers with no factor…

A:

Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: If f (x) = 3x²-2 4x+1 then f'(-1) =

A: Given

Q: x³ + x 10) √ (x²+ + 2x² + 5) dx

A:

Q: why does F(r(t))=-r/(1+(a-1)t)^3/2 instead of r^3? does |r| just equals to 1+(a-1)t?

A:

Q: 2x+6)dx x²+2x+5

A:

Q: る(4xナx)(10x2+x2-2

A:

Q: x3 – 3x2 – 6x - Show that - = x-3 - x2 – 9 x – 3'x +3* - - x3 - 3x2 - 6x -dxp. Hence, evaluate x2 -…

A: To show: The equation x3-3x2-6xx2-9=x-3-3x-3+6x+3 and then evaluate the integral ∫x3-3x2-6xx2-9.…

Q: If u(x) = x3, then du = 3x2.

A:

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: Let f(x) = -2x√√x + f'(x) = -8 x²√x

A:

Q: f"(2) 1. Find

A: Given f(x)=43x2-23x+1f'(x)=-23*ddx(x)+43*ddx1x2+ddx(1)        =-2*13+4(-2)x-33+0

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

A: