Name Date

Calculus Independent Study Path Unit Test 3.1

1. Differentiate

y = sin (cos [(x^{2} + 3x)^{40}])

with respect to x.

2. Find \frac{dy}{dx}:

x + sin y = y + cos x.

3. Find a tangent line to

y = cos(sin 3x)

passing through the point (0,1).

4. Find D_{x} sin^{2} x, D_{x} sin^{3} x, and D_{x} sin^{4} x. What is D_{x} sin x^{n} ?

5. Find \frac{dy}{dx}:

sin x = cos(sin y)

6. Find \frac{ds}{dr}:

1 = (tan sr)

7. Prove the product rule for rational exponents by implicitly differentiating y^{n} = x^{m} (where n and m are integers).