Determine the Derivatives f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))]

Name: Determine the Derivatives f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))]
Uploaded: 2022-02-23T17:22:57+00:00
Description: Determine the Derivatives f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))]

Question

Brighton · Accepted Answer

Solution:Given: The function is f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))].Rewrite the function:f(x)=sin⁡h(cot⁡h(sin⁡h(x2)))Differentiate f with respect to x:ddxf(x)=cos⁡h(cot⁡h(sin⁡h(x2)))ddx(cot⁡h(sin⁡h(x2)))=cos⁡h(cot⁡h(sin⁡h(x2)))(−csc⁡h2(sin⁡h(x2)))ddx(sin⁡h(x2))=−csc⁡h2(sin⁡h(x2))cos⁡h(cot⁡h(sin⁡h(x2)))cos⁡h(x2)ddx(x2)=−csc⁡h2(sin⁡h(x2))cos⁡h(cot⁡h(sin⁡h(x2)))cos⁡h(x2)(2x)Conclusion:Therefore, the derivative is f′(x)=−2xcsc⁡h2(sin⁡h(x2))cos⁡h(cot⁡h(sin⁡h(x2)))cos⁡h(x2).

Jeffrey Jordon · Accepted Answer

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Determine the Derivatives f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))]

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