Questions from General Calculus

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 (1, e).

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

Find the equation of the tangent line to the curve y = ex/(1 + 2ex) at (0, 1/3).

Q: Differentiate the function. y = √x + 2(

Differentiate the function. y = √x + 2(2x + 1)2

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

Find the equation of the tangent line to the curve y = ex/(x + ex) at (0, 1).

Q: Differentiate the functions. y = (x + 3)

Differentiate the functions. y = (x + 3) / (2x + 1)2

Q: Find the first and second derivatives. f (x)

Find the first and second derivatives. f (x) = ex(1 + x)2

Q: Find the first and second derivatives. f (x)

Find the first and second derivatives. f (x) = ex/x

Q: Compute the following derivatives. (a) d/dx

Compute the following derivatives. (a) d/dx (5ex) (b) d/dx (ex)10 (c) Use the fact that e2+x = e2 * ex to find d/dx (ex+2).

Q: Compute the following derivatives. (a) Use the fact

Compute the following derivatives. (a) Use the fact that e4x = (ex)4 to find d/dx (e4x). Simplify the derivative as much as possible. (b) Take an approach similar to the one in (a) and show that, if k...

Q: Sketch the graphs of the following functions. y = e2x

Sketch the graphs of the following functions. y = e2x