The Power Rule and Basic Differentiation Rules Worksheet with Answer Key

What's on the worksheet

1. Find each derivative with the power, constant multiple, sum and constant rules.
   y = x^{15}y = -\dfrac{2}{3}x^{9}\dfrac{d}{dt}\big[4t^5 - t^2\big]y = \dfrac{x^6}{3} - 5x^2 + 8y = 3x^4 - 7x^3 + \dfrac{1}{2}x^2 - x + 12
2. Rewrite each function as a sum of constant multiples of powers of x, then find dydx.
   y = \dfrac{7}{x^3}y = \sqrt[5]{x^2}y = \dfrac{1}{4x^2}y = x^2\sqrt{x}y = \dfrac{3x^3 - 2x + 5}{x^2}
3. The curve y = ax³ + bx², where a and b are constants, has slope −17 at x = 1 and slope −52 at x = 2.
4. Lucas rewrites each function as a power of x and then uses the power rule, but each line has one mistake.
5. Let $f