Questions from General Calculus

Q: Use the definition of a derivative to find f'(x)

Use the definition of a derivative to find f'(x) and f''(x). Then graph f, f', and f'' on a common screen and check to see if your answers are reasonable. f (x) = x3 - 3x

Q: Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function. y = √xx

Q: Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function. y = (tan x)1/x

Q: Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function. y = (sin x) lnx

Q: Find y' if y = ln (x2 + y2).

Find y' if y = ln (x2 + y2).

Q: Find y' if xy = yx.

Find y' if xy = yx.

Q: Find a formula for f(n)(x) if f

Find a formula for f(n)(x) if f (x) = ln (x - 1).

Q: Find d9/dx9 (x8 ln x).

Find d9/dx9 (x8 ln x).

Q: Use the definition of derivative to prove that limx→0 ln

Use the definition of derivative to prove that limx→0 ln (1 + x)/x = 1

Q: Show that limx→∞ (1 + x/n) n

Show that limx→∞ (1 + x/n) n for any x > 0.