Slide16.JPG

Slide17.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 29 Differentiate π‘₯^sin⁑π‘₯ , π‘₯ > 0 𝑀.π‘Ÿ.𝑑. π‘₯.Let y = π‘₯^sin⁑π‘₯ Taking log both sides log⁑𝑦 = log π‘₯^sin⁑π‘₯ π’π’π’ˆβ‘π’š = π’”π’Šπ’β‘π’™ . π’π’π’ˆ 𝒙 Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ (𝑑(log⁑〖𝑦)γ€—)/𝑑π‘₯ = 𝑑/𝑑π‘₯ (sin⁑〖π‘₯ log⁑π‘₯ γ€— ) By product Rule (uv)’ = u’v + v’u where u = sin x & v = log x (𝑑(log⁑〖𝑦)γ€—)/𝑑π‘₯ = (𝑑(sin⁑π‘₯))/𝑑π‘₯.log π‘₯+sin π‘₯ . (𝑑(log⁑π‘₯))/𝑑π‘₯ (𝑑(log⁑〖𝑦)γ€—)/𝑑𝑦 Γ— 𝑑𝑦/𝑑π‘₯ = cos⁑π‘₯ log⁑π‘₯ + sin⁑π‘₯ 1/π‘₯ 𝑑𝑦/𝑑π‘₯ 1/𝑦 = 𝒄𝒐𝒔 π’™β‘π’π’π’ˆβ‘π’™ + π’”π’Šπ’β‘π’™ 𝟏/𝒙 𝑑𝑦/𝑑π‘₯ = 𝑦 (γ€–π‘π‘œπ‘  π‘₯γ€—β‘γ€–π‘™π‘œπ‘”β‘γ€–π‘₯+1/π‘₯γ€— 𝑠𝑖𝑛⁑π‘₯ γ€— ) Putting back 𝑦 = π‘₯^𝑠𝑖𝑛⁑π‘₯ 𝑑𝑦/𝑑π‘₯ = π‘₯^𝑠𝑖𝑛⁑π‘₯ (cos⁑〖log⁑〖π‘₯+ 1/π‘₯γ€— sin⁑π‘₯ γ€— ) = π‘₯^𝑠𝑖𝑛⁑π‘₯ cos⁑log⁑π‘₯ + π‘₯^𝑠𝑖𝑛⁑π‘₯ 1/π‘₯ 𝑠𝑖𝑛⁑π‘₯ = π‘₯^𝑠𝑖𝑛⁑π‘₯ cos⁑log⁑π‘₯ + π‘₯^𝑠𝑖𝑛⁑π‘₯ π‘₯^(βˆ’1) sin⁑π‘₯ = 𝒙^π’”π’Šπ’β‘π’™ π’„π’π’”β‘π’π’π’ˆβ‘π’™ + 𝒙^π’”π’Šπ’β‘γ€–π’™ βˆ’ πŸγ€— π’”π’Šπ’β‘π’™

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.