What is the derivative of ln(sin(x^2+4))

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of `ln(sin(x^2 + 4))` has to be determined. Use the chain rule. The derivative is:

`(ln(sin(x^2 + 4)))'*(sin(x^2 + 4))'*(x^2 + 4)'`

=> `1/(sin(x^2 + 4))*cos(x^2 + 4)*2x`

=> `2x*(cos(x^2+4)/(sin(x^2+4)))`

=> `2x*cot(x^2 + 4)`

The derivative of `ln(sin(x^2 + 4))` is `2x*cot(x^2 + 4)`

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