Questions from General Calculus

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 [ g ( g (x))] |x=1

Q: Let f (x), g (x), and h (

Let f (x), g (x), and h (x) be differentiable functions. Find a formula for the derivative of f (x)g (x)h (x).

Q: Find a formula for d/dx f (g (x

Find a formula for d/dx f (g (x)), where f (x) is a function such that f (x) = x√(1 - x2). g (x) = x2

Q: Find a formula for d/dx f (g (x

Find a formula for d/dx f (g (x)), where f (x) is a function such that f (x) = x√(1 - x2). g (x) = √x

Q: Find a formula for d/dx f (g (x

Find a formula for d/dx f (g (x)), where f (x) is a function such that f (x) = x√(1 - x2). g (x) = x3/2

Q: Find dy/dx, where y is a function of u

Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x only. u = x3/2

Q: Find dy/dx, where y is a function of u

Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x only. u = x2 + 1

Q: Find dy/dx, where y is a function of u

Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x only. u = 5/x

Q: Find dy/dx, where y is a function of u

Find dy/dx, where y is a function of u such that dy/du = u/√(1 + u4). u = x2

Q: Find dy/dx, where y is a function of u

Find dy/dx, where y is a function of u such that dy/du = u/√(1 + u4). u = √x