Rule No. 3: If y = kx, then = k (where k is a constant)Rule No. 4: If y = k, then = 0 (where k is a constant)Note: For future reference, a, b, c, n, and k always stand for constants.
Example 7: If y = 8x^4 , then = 32x^3.
Example 8: If y = 5x^100 , then y′ = 500x^99.
Example 9: If y = −3x−5, then = 15x−6.
Example 10: If f(x) = 7x, then f′(x) = .
Example 11: If y = x , then = .
Example 12: If y = 12, then = 0.
If you have any questions about any of these 12 examples (especially the last two), review the rules. Now
for one last rule.
THE ADDITION RULE
If y = axn + bxm, where a and b are constants, then = a(nxn−1) + b(mxm−1)This handy rule works for subtraction too.