Derivative of Absolute Value of Tanx :
In this section, we will learn, how to find the derivative of absolute value of (tanx).
Let |f(x)| be the absolute-value function.
Then the formula to find the derivative of |f(x)| is given below.
Based on the formula given, let us find the derivative of absolute value of tanx.
Derivative of |tanx| :
|tanx|' = [tanx/|tanx|] ⋅ (tanx)'
|tanx|' = [tanx/|tanx|] ⋅ sec²x
|tanx|' = sec2x ⋅ tanx / |tanx|
Derivative of |sinx| :
|sinx|' = [sinx/|sinx|] ⋅ (sinx)'
|sinx|' = [sinx/|sinx|] ⋅ cosx
|sinx|' = (sinx ⋅ cosx) / |sinx|
Derivative of |cosx| :
|cosx|' = [cosx/|cosx|] ⋅ (cosx)'
|cosx|' = [cosx/|cosx|] ⋅ (-sinx)
|cosx|' = - (sinx ⋅ cosx) / |cosx|
Derivative of |cscx| :
|cscx|' = [cscx/|cscx|] ⋅ (cscx)'
|cscx|' = [cscx/|cscx|] ⋅ (-cscx ⋅ cotx)
|cscx|' = - (csc2x ⋅ cotx) / |cscx|
Derivative of |secx| :
|secx|' = [secx/|secx|] ⋅ (secx)'
|secx|' = [secx/|secx|] ⋅ (secx ⋅ tanx)
|secx|' = - (sec2x ⋅ tanx) / |secx|
Derivative of |cotx| :
|cotx|' = [cotx/|cotx|] ⋅ (cotx)'
|cotx|' = [cot/|cotx|] ⋅ (-csc2x)
|cotx|' = - (csc2x ⋅ cotx) / |cotx|
After having gone through the stuff given above, we hope that the students would have understood, how to find derivative of absolute value of tanx.
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