AP Calculus Power, Product and Quotient Rule Derivatives

Calculus - Product Rule, Quotient Rule, Power Rule #calculus #calcderivativerules #productrule #quotientrule #powerrule

Questions 6

Answers

1
j(x)=(5x-2)/(2-4x)
(-40x+2)/(2-4x)2
2
2/(2-4x)2
I've forgotten the Product Rule
2
Find the derivative of y = 3/x + x²/3 .
-3 + (2/3) x
3 + 2x/3
3 + 6x
-3/x2 +(2/3) x
3
Find the derivative of g(x)=(3x-2)/(x²+2)
(3x2-4x-6)/(x2+2)2
(-3x2+4x+6)/(x2+2)2
9x2+2
This is impossible
4
p(x)=(4x²+2)(3-7x)
(-28x2+24x+14)/(3-7x)2
-84x2+24x-14
-28x2+24x+14
(-84x2+24x-14)/(3-7x)2
5
Find the derivative of f(x) = x³- 2x²+ 5x - 6
x2 - 4x + 5
3x2 - 4x + 5 - 1
3x2 - 4x + 5
3x2 - 4x
6
h(x)=(3x+2)(5x³+2x)
-30x3-30x2-4
I give up
60x3+30x2+12x+4
45x2+6

Calculus - Product Rule, Quotient Rule, Power Rule #calculus #calcderivativerules #productrule #quotientrule #powerrule

Answers

1
j(x)=(5x-2)/(2-4x)
(-40x+2)/(2-4x)2
2
2/(2-4x)2
I've forgotten the Product Rule
2
Find the derivative of y = 3/x + x²/3 .
-3 + (2/3) x
3 + 2x/3
3 + 6x
-3/x2 +(2/3) x
3
Find the derivative of g(x)=(3x-2)/(x²+2)
(3x2-4x-6)/(x2+2)2
(-3x2+4x+6)/(x2+2)2
9x2+2
This is impossible
4
p(x)=(4x²+2)(3-7x)
(-28x2+24x+14)/(3-7x)2
-84x2+24x-14
-28x2+24x+14
(-84x2+24x-14)/(3-7x)2
5
Find the derivative of f(x) = x³- 2x²+ 5x - 6
x2 - 4x + 5
3x2 - 4x + 5 - 1
3x2 - 4x + 5
3x2 - 4x
6
h(x)=(3x+2)(5x³+2x)
-30x3-30x2-4
I give up
60x3+30x2+12x+4
45x2+6