Question

find the derivation of ( sin x + cos x) using first principal​

Answer 1

Answer:

What is the derivative of sinx + cosx using first principle?

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First principle is commonly written as

df(x)dx=limh→0f(x+h)−f(x)h

d(sinx+cosx)dx=limh→0sin(x+h)+cos(x+h)−(sinx+cosx)h

=limh→0sin(x+h)−sinx+cos(x+h)−cosxh

=limh→0sin(x+h)−sinxh+limh→0cos(x+h)−cosxh

=limh→02cos((x+h)+x2)sin((x+h)−x2)h+limh→0−2sin((x+h)+x2)sin((x+h)−x2)h

=limh→0cos(2x+h2)sin(h2)h/2+limh→0−sin(2x+h2)sin(h2)h/2

, Therefore it becomes

=cosx−sinx

I hope it helps