Finding derivative of a function by chain rule
Finding derivative of a function by chain rule
Last updated at Aug. 13, 2021 by Teachoo
Misc 8 Differentiate π€.π.π‘. π₯ the function, cos β‘(π cosβ‘π₯+π sinβ‘π₯), for some constant π and π. Let π¦ = cos β‘(π cosβ‘π₯+π sinβ‘π₯) Differentiating π€.π.π‘.π₯. ππ¦/ππ₯ = (π(cos((a cosβ‘x+b sinβ‘x )))/ππ₯ ππ¦/ππ₯ = βsinβ‘π₯ (π cosβ‘π₯+π sinβ‘π₯) . (πβ‘(π cosβ‘π₯+π sinβ‘π₯))/ππ₯ = βsinβ‘π₯ (π cosβ‘π₯+π sinβ‘π₯) . (π .πβ‘(cosβ‘π₯ )/ππ₯+π .πβ‘(sinβ‘π₯ )/ππ₯) = βsinβ‘π₯ (π cosβ‘π₯+π sinβ‘π₯) . (π(βsinβ‘π₯ )+π (cosβ‘π₯ )) = βsinβ‘π₯ (π cosβ‘π₯+π sinβ‘π₯) . (βπ sinβ‘π₯+π cosβ‘π₯ ) = βsinβ‘π₯ (π cosβ‘π₯+π sinβ‘π₯) . β(π sinβ‘π₯βπ cosβ‘π₯ ) = π¬π’π§β‘γ (π πππβ‘π+π πππβ‘π)" " (π πππβ‘πβπ πππβ‘π )γ