## DERIVATIVE OF ABSOLUTE VALUE OF SIN X

Derivative of Absolute Value of Sinx :

In this section, we will learn, how to find the derivative of absolute value of (sinx)

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 sinx.

Derivative of |sinx| :

|sinx|'  =  [sinx/|sinx|]  (sinx)'

|sinx|'  = [sinx/|sinx|]  cosx

|sinx|'  =  (sinx ⋅ cosx) / |sinx|

## Derivative of Absolute Value of Other Trigonometric Functions

Derivative of |cosx| :

|cosx|'  =  [cosx/|cosx|]  (cosx)'

|cosx|'  =  [cosx/|cosx|]  (-sinx)

|cosx|'  =  - (sinx ⋅ cosx) / |cosx|

Derivative of |tanx| :

|tanx|'  =  [tanx/|tanx|]  (tanx)'

|tanx|'  = [tanx/|tanx|] ⋅ sec²x

|tanx|'  =  sec2⋅ tanx / |tanx|

Derivative of |cscx| :

|cscx|'  =  [cscx/|cscx|]  (cscx)'

|cscx|'  =  [cscx/|cscx|]  (-cscx  cotx)

|cscx|'  =  - (csc2⋅ cotx) / |cscx|

Derivative of |secx| :

|secx|'  =  [secx/|secx|]  (secx)'

|secx|'  =  [secx/|secx|]  (secx  tanx)

|secx|'  =  - (sec2⋅ tanx) / |secx|

Derivative of |cotx| :

|cotx|'  =  [cotx/|cotx|]  (cotx)'

|cotx|'  =  [cot/|cotx|]  (-csc2x)

|cotx|'  =  - (csc2⋅ 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 sinx.

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