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7-97.

Find $\frac { d y } { d t }$ for each of the following functions.

$y = \frac { ( 3 x ^ { 2 } - 2 ) ^ { 3 } } { - 2 }$
Hint (a):
This is NOT a Quotient Rule problem!
Step 1(a):
Before differentiating, rewrite the equation as $y=-\frac{1}{2}(3x^{2}-2)^{3}.$

$y = 6^{(3x^2 − 2)^3}$
Answer (b):
^{$= 18\operatorname{ln}(6)x(3x^2 − 2)^2\ 6^{(3x2 − 2)3}$}

$(2y)^2 −\operatorname{cos}(x^5) = 9$
Hint (c):
Use implicit differentiation.

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