Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Finding derivative of Implicit functions
Last updated at May 29, 2023 by Teachoo
Ex 5.3, 8 Find 𝑑𝑦/𝑑𝑥 in, sin2 𝑥 + cos2 𝑦 = 1 sin2 𝑥 + cos2 𝑦 = 1 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . (𝑑 (sin2 𝑥 + cos2 𝑦))/𝑑𝑥 = (𝑑 (1))/𝑑𝑥 (𝑑 (sin2 𝑥))/𝑑𝑥 + (𝑑 (cos2 𝑦))/𝑑𝑥 = 0 Calculating Derivative of sin2 𝑥 & cos^2 𝑦 sepretaly Finding Derivative of 𝒔𝒊𝒏𝟐 𝒙 (𝑑 (sin2 𝑥))/𝑑𝑥 =2〖 𝑠𝑖𝑛〗^(2−1) 𝑥 . (𝑑(sin^2𝑥))/𝑑𝑥 =2 sin𝑥 . (𝑑(sin𝑥))/𝑑𝑥 (Derivative of constant is 0) =2 sin〖𝑥 〖 cos〗𝑥 〗 Finding Derivative of 〖𝒄𝒐𝒔〗^𝟐 𝒚 (𝑑 (cos2 𝑦))/𝑑𝑥 =2〖cos𝑦〗^(2−1) ". " 𝑑/𝑑𝑥 " "(cos𝑦) =2 cos𝑦 . (−sin𝑦) . (𝑑(𝑦))/𝑑𝑥 =− 2 cos𝑦 sin𝑦 . 𝑑𝑦/𝑑𝑥 Now, (𝑑 (sin2 𝑥))/𝑑𝑥+ (𝑑 (cos2 𝑦))/𝑑𝑥 = 0 2 sin𝑥 .cos𝑥 + (− 2 cos𝑦 sin𝑦 ". " 𝑑𝑦/𝑑𝑥)= 0 2 sin𝑥 .cos𝑥 − 2 sin𝑦〖 .〗 cos𝑦 . 𝑑𝑦/𝑑𝑥 = 0 − 2 sin𝑦〖 .〗 cos𝑦 . 𝑑𝑦/𝑑𝑥 = − 2 sin𝑥 cos𝑥 − sin2𝑦〖 .〗 𝑑𝑦/𝑑𝑥 = − sin2𝑥 𝑑𝑦/𝑑𝑥 = 〖− sin〗2𝑥/(−sin2𝑦 ) 𝒅𝒚/𝒅𝒙 = 𝒔𝒊𝒏𝟐𝒙/𝒔𝒊𝒏𝟐𝒚 (2 sin x cos x = sin 2x)