Determine the derivative  `(dr)/(d theta)`  for `r=tan^2(3-theta^3)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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For` r = tan^2(3 - theta^3)` the derivative `(dr)/(d theta)` has to be determined. Use the chain rule.

`(dr)/(d theta)` = `2*tan(3 - theta^3)*sec^2(3 - theta^3)*(-3*theta^2)`

=> `-6*theta^2*tan(3 - theta^3)*sec^2(3 - theta^3)`

The derivative `(dr)/(d theta)` for` r = tan^2(3 - theta^3)` is `(dr)/(d theta) = -6*theta^2*tan(3 - theta^3)*sec^2(3 - theta^3)`

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