Question
If y = e^x cosx, prove that dy/dx sqrt(2) e^x . cos(x+ pie/4)
Answers
Reiny
The simple dy/dx = e^x(-sinx) + e^xcosx
= e^x(cosx - sinx)
RS = √2(e^x)(cos(x+π/4)
= √2(e^x)(cosxcosπ/4 - sinxsinπ/4)
= √2(e^x)(cosx(1/√2 - sinx(1/√2)
= e^x (cosx - sinx)
= the dy/dx from above
= e^x(cosx - sinx)
RS = √2(e^x)(cos(x+π/4)
= √2(e^x)(cosxcosπ/4 - sinxsinπ/4)
= √2(e^x)(cosx(1/√2 - sinx(1/√2)
= e^x (cosx - sinx)
= the dy/dx from above