Class 12th Calculus
posted by Akash .
If y = e^x cosx, prove that dy/dx sqrt(2) e^x . cos(x+ pie/4)

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