Questions from General Calculus

Q: Differentiate the function. y = √ [(x + 3

Differentiate the function. y = √ [(x + 3)/(x2 + 1)]

Q: Differentiate the following functions. y = (ex – 1

Differentiate the following functions. y = (ex – 1)/(ex + 1)

Q: Differentiate the following functions. y = 2ex + 1

Differentiate the following functions. y = 2ex + 1

Q: Radioactive cobalt 60 has a half-life of 5.3

Radioactive cobalt 60 has a half-life of 5.3 years. Find its decay constant.

Q: The graph of y = x - ex has one extreme point

The graph of y = x - ex has one extreme point. Find its coordinates and decide whether it is a maximum or a minimum.

Q: Find the extreme points on the graph of y = x2ex,

Find the extreme points on the graph of y = x2ex, and decide which one is a maximum and which one is a minimum.

Q: Find the point on the graph of y = (1 +

Find the point on the graph of y = (1 + x2)ex where the tangent line is horizontal.

Q: Show that the tangent line to the graph of y = ex

Show that the tangent line to the graph of y = ex at the point (a, ea) is perpendicular to the tangent line to the graph of y = e-x at the point (a, e-a).

Q: Find the slope of the tangent line to the curve y =

Find the slope of the tangent line to the curve y = xex at (0, 0).

Q: Compute the given derivatives with the help of formulas (1)–(

Compute the given derivatives with the help of formulas (1)–(4). (a) d/dx (2x) |x=1/2 (b) d/dx (2x) |x=2