Limits and Derivatives

Limits and Derivatives

Question

Find the derivatives of the following functions :

sin x cos x

Answer

Let y sin x cos x 
Differentiating both sides w.r.t.  x,  we get

space space space space space space space space space space space space space space space space space space space space space space space space dy over dx space equals space straight d over dx left parenthesis sin space straight x space cos space straight x space right parenthesis space equals space sin space straight x space straight d over dx left parenthesis cos space straight x right parenthesis space plus space cos space straight x straight d over dx left parenthesis sin space straight x right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space sin space straight x left parenthesis negative sin space straight x right parenthesis space plus space cos space straight x left parenthesis cos space straight x right parenthesis space equals space minus space sin squared straight x plus cos squared straight x

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space cos squared straight x minus sin squared straight x equals cos 2 straight x

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