Question

❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​

Answer 1

Answer:

4cis(4x+5)

Explanation:

f(x)=sin(4x+5)

f'(x)= derivative of sin(4x+5) × derivative of 4x+5

= cos (4x+5) × 4

Answer 2

Answer:

4cos(4x+5)

Explanation:

Using chain rule first derivate the sin (theta) portion

Then derivate the (4x+5) portion and then multiply both.

As we know derivative of sin (theta) is cos (theta) and derivative of (4x+5) will come out to be 4×1 + 0 = 4, thus,

f(x) = sin(4x+5)

f'(x) = cos(4x+5) × 4 = 4cos(4x+5)