Question

Find the derivatives of these:

f(x)=(√(x))sinPix

Also:

f(x)=√(Cosx+sinx)

Steps would be greatly helpful as I will be able to use them as reference. Thank you.

Answer 1

f'(x)=(√(x))'*(sin(pix))+(sin(pix))'*(√(x))=1/2*(x)^(-1/2)*(sin(pix))+cos(pix)*(pi)*(√(x))

2)
f'(x)=(1/2(cosx+sinx)^(-1/2))(cos(x)+sin(x))'=(1/2(cosx+sinx)^(-1/2)*(-sin(x)+cos(x))

Answer 2

correct answers, but they're sort of like leaving an answer as 4x^2y/3xy instead of simplifying to 4x/3

1)1/2√x sinπx + π/√x cosπx
= 1/2√x (sinπx + 2πcosπx)

2)
(cosx-sinx) / 2√(cosx+sinx)