Combining Differentiation Rules Worksheet with Answer Key

What's on the worksheet

1. For each function, name the outermost operation (the one done last when you compute the function at a number), then differentiate.
   y = x^2 e^{3x}y = \cos^3(2x)y = \sec\sqrt{x}y = \dfrac{\ln x}{x^2}y = \arctan\left(e^{x}\right)
2. Rewrite y = 4x³ + 3x² - 12x² as a sum of powers of x.
3. Let y = x² - 9x² + x - 6.
4. Let y = 6x² e^x for x ≠ 0.
5. The functions f and g are differentiable, with these values.
6. 1 2 3 4 5 6 7 1 2 3 4 5 0 x y y = f