Questions from General Calculus

Q: Differentiate the following functions. y = √x/(√x

Differentiate the following functions. y = √x/(√x + 4)

Q: Differentiate the following functions. y = 3(x2 -

Differentiate the following functions. y = 3(x2 - 1)3(x2 + 1)5

Q: Differentiate the following functions. y = 1/(x2 +

Differentiate the following functions. y = 1/(x2 + 5x + 1)6

Q: Differentiate the following functions. y = (x2 - 6x

Differentiate the following functions. y = (x2 - 6x)/(x – 2)

Q: Differentiate the following functions. y = 2x/(2 -

Differentiate the following functions. y = 2x/(2 - 3x)

Q: Differentiate the following functions. y = [(3 - x2

Differentiate the following functions. y = [(3 - x2)/x3]2

Q: Differentiate the following functions. y = (x3 + x

Differentiate the following functions. y = (x3 + x)/(x2 – x)

Q: Let f (x) = (3x + 1)4

Let f (x) = (3x + 1)4(3 - x)5. Find all x such that f ‘(x) = 0.

Q: The derivative of (x3 - 4x)>x is obviously 2x

The derivative of (x3 - 4x)>x is obviously 2x for x ≠ 0, because (x3 - 4x)/x = x2 ≠ 4 for x  0. Verify that the quotient rule gives the same derivative.

Q: Given f (1) = 1, f ‘(1

Given f (1) = 1, f ‘(1) = 5, g (1) = 3, g’(1) = 4, f ‘(3) = 2, and g ‘(3) = 6, compute. d/dx [ f ( f (x))] |x=1