### Home > CALC > Chapter 5 > Lesson 5.3.1 > Problem 5-112

5-112.

Differentiate the functions. Homework Help ✎

*y*= tan(*x*^{2}+ 3)*y*=*−*5(*x*− 3)^{8}*y*=*x*tan(*x*^{2}+ 3)

Do NOT use the quotient rule (though it will work). This is a Power Rule problem: *y* = −2*x*^{−3}. Reserve the Quotient Rule for situations in which there are variables in BOTH the numerator and the denominator.

Chain Rule.

This is not technically a Chain Rule problem, though you may use it.

This calls for the Quotient Rule.

Product Rule & Chain Rule combined.

Refer to the hint in part (a). And recall that the reciprocal of cos*x* is sec*x*.