Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. y = (3-x²) (x³ -x+1) = (3-x²) and v= a. Apply the Product Rule. Let u= d (uv) = (3-x²)+(x³ -x+1) O v= (x³ -x+1).

Q: factor this derivative: 2/3x-1/3(x+4)2+x2/3 2(x+4). must show all steps

A: Solution -    Given equation -  f(x) = 23 x-13x+42+2 x23(x+4) = 0 f(x) = 2 x+423 x13+2 x23(x+4) = 0…

Q: 11- +2 = x² y6 dx x ech

A:

Q: Find - 6x+1 x² +1 -dx.

A:

Q: Evalvate 5x-12 X (x²+4) dx

A:

Q: f. S r4 dx J2 xV2-2x2 2.

A:

Q: Write y=2(0.5x-6)(6-24x) in the form y=k(x-r)(x-s) and give the values of k,r,s.

A: We have to factor out 0.5 and -24

Q: (√3-3)/6 - (√3+3) /6 12 dx 2 1+ (2x + 1)²

A:

Q: 3hx 3x 2. २ +२ ८

A: As per the guidelines I have to do a maximum of 1 question so I request you to submit the remaining…

Q: Vx² - 2x + 3 dx

A:

Q: Simplify V(5/2)=(4/3)(pi)(r)^3 and V(4r)=(4/3)(pi)(r)^3

A: We need to find the volume of a sphere with (A) radius = 5/2 units and (B) radius = 4r units.We know…