Use the chain rule to find the derivative dy/dx for each of the following functions of a function.

Check each answer on your own with the generalized power function rule, noting that the generalized power function rule is simply a specialized use of the chain rule.

Transcribed Image Text:

(a) y = (2x+9)7 Let yu7 and u = 2x5 +9. Then dy/du: =7u6 and du/dx: 10x4. From the chain rule in (9.6), Substituting, But u 2x5 +9. Substituting again, = (b) y (6x+1) dy == dx dy dy du = dx du dx 7u6 10x470x+u6 . dy = 70x4(2x+9)6 dx = Let yu and u = 6x + 1, then dy/du =2u and du/dx = 6. Substituting these values in the chain rule, dy =2u 6=12u dx