Calculus I, Fall 2013

Quiz 2

Oct 17, 2013 Show all details.

1. Evaluate \frac{d^{4}}{dx^{4}} (x^{4} cos(x − 1))|_{x=1}.

2. Find the derivative of y = sin^{2}(tan(x^{3})). Need not simplify your final expression.

3. Suppose we know that \frac{d}{dx}x^{n} = nx^{n−1} for all integers n. Show that this is also true for n = q/p where p, q are integers and p ≠ 0.

4. Use implicit differentiation (and not other methods) to find dy/dx and d^{2}y/dx^{2} at (1, 1) where y(x) is implicitly given by x^{4} + y^{4} = 2.

5. True or False? (prove it if true, correct it if false).

Let g be the inverse function of f and \frac{d}{dx}f(x) = f_{1}(x), \frac{d}{dx}g(x) = g_{1}(x).

Then f_{1}(x)g_{1}(x) = 1.

Calculus I, Fall 2013

Quiz 2

Oct 17, 2013 Show all details.

1. Evaluate \frac{d^{4}}{dx^{4}} (x^{4} cos(x − 1))|_{x=1}.

2. Find the derivative of y = sin^{2}(tan(x^{3})). Need not simplify your final expression.

3. Suppose we know that \frac{d}{dx}x^{n} = nx^{n−1} for all integers n. Show that this is also true for n = q/p where p, q are integers and p ≠ 0.

4. Use implicit differentiation (and not other methods) to find dy/dx and d^{2}y/dx^{2} at (1, 1) where y(x) is implicitly given by x^{4} + y^{4} = 2.

5. True or False? (prove it if true, correct it if false).

Let g be the inverse function of f and \frac{d}{dx}f(x) = f_{1}(x), \frac{d}{dx}g(x) = g_{1}(x).

Then f_{1}(x)g_{1}(x) = 1.