how can we find derivative of x^sinx+(sinx)^cosx??
 

Asked by ganeshgawali59 | 4th Jul, 2016, 09:32: PM

Expert Answer:

begin mathsize 12px style straight d over dx open square brackets straight x to the power of sinx plus sin to the power of cosx left parenthesis straight x right parenthesis close square brackets
equals straight d over dx open square brackets straight x to the power of sinx close square brackets space plus straight d over dx open square brackets sin to the power of cosx left parenthesis straight x right parenthesis close square brackets
equals straight x to the power of sinx straight d over dx open square brackets ln left parenthesis straight x right parenthesis sinx close square brackets plus sin to the power of cosx left parenthesis straight x right parenthesis straight d over dx open square brackets ln left parenthesis sinx right parenthesis cosx close square brackets
equals straight x to the power of sinx open parentheses straight d over dx open square brackets lnx close square brackets times sinx plus straight d over dx sinx times ln left parenthesis straight x right parenthesis close parentheses plus sin to the power of cosx left parenthesis straight x right parenthesis open parentheses straight d over dx open square brackets ln left parenthesis sinx right parenthesis close square brackets times cosx plus straight d over dx cosx times ln left parenthesis sinx right parenthesis close parentheses
equals straight x to the power of sinx open parentheses sinx over straight x plus times ln left parenthesis straight x right parenthesis cosx close parentheses plus sin to the power of cosx left parenthesis straight x right parenthesis open parentheses cosx over sinx straight d over dx sinx minus sinx times ln left parenthesis sinx right parenthesis close parentheses
equals straight x to the power of sinx open parentheses sinx over straight x plus times ln left parenthesis straight x right parenthesis cosx close parentheses plus sin to the power of cosx left parenthesis straight x right parenthesis open parentheses fraction numerator cos squared straight x over denominator sinx end fraction minus sinx times ln left parenthesis sinx right parenthesis close parentheses end style

Answered by Rebecca Fernandes | 5th Jul, 2016, 10:46: AM