Question

find delta (x+cos x)?​

Answer 1

Answer:

ʏᴏᴜ ᴄᴀɴ ᴅᴇʀɪᴠᴇ ᴛʜᴇ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏғ sɪɴ(x)

ʟᴇᴛ ʏ = sɪɴ(x)

ʏ + ᴅᴇʟᴛᴀ ʏ = sɪɴ(x + ᴅᴇʟᴛᴀ x)

sɪɴ(x + ᴅᴇʟᴛᴀ x)

= sɪɴx*ᴄᴏs(ᴅᴇʟᴛᴀ x) + ᴄᴏsx*sɪɴ(ᴅᴇʟᴛᴀ x)

(ᴅᴇʟᴛᴀ ʏ)/(ᴅᴇʟᴛᴀ x) = sɪɴ(x+ᴅᴇʟᴛᴀ x) - sɪɴ(x)

(ᴅᴇʟᴛᴀ ʏ) =sɪɴx*ᴄᴏs(ᴅᴇʟᴛᴀ x) + ᴄᴏsx*sɪɴ(ᴅᴇʟᴛᴀ x) - sɪɴx

ᴀs ᴅᴇʟᴛᴀ x ᴀᴘᴘʀᴏᴀᴄʜᴇs ᴢᴇʀᴏ, ᴅᴇʟᴛᴀ ʏ = ᴄᴏsx*ᴅᴇʟᴛᴀ x, (ᴅᴇʟᴛᴀ ʏ)/(ᴅᴇʟᴛᴀ x) = ᴅʏ/ᴅx

(ᴅᴇʟᴛᴀ ʏ)/(ᴅᴇʟᴛᴀ x) = ᴅʏ/ᴅx= ᴄᴏsx*ᴅᴇʟᴛᴀ x/ᴅᴇʟᴛᴀ x = ᴄᴏsx

Answer 2

Answer:

Use the formula, d/dx(u*v) = u* d/dx(v) + v* d/dx(u)

d/dx(x*cosx)

= x* d/dx(cosx) + cosx* d/dx(x)

=x*(-sinx) + coSX * 1

= -x.sinx + COSX