Question

u =x^2-y^2-Sinyz if y=e^x and z=logx find du/dx​

Answer 1

Given :  u = x² - y² - sinyz    

y = eˣ  and  z = ln x  

To Find :  du/dx​

Solution:

u = x² - y² - sinyz    

=> du/dx = 2x  - 2y.dy/dx   - Cosyz( y.dz/dx + z.dy/dx)

y = eˣ

=> dy/dx  =  eˣ

z = ln x

=> dz/dx = 1/x

du/dx = 2x  - 2y.dy/dx   - Cosyz( y.dz/dx + z.dy/dx)

=> du/dx = 2x  - 2eˣ.eˣ   - Cos( eˣ. ln x )(  eˣ/x +  ln x .eˣ)

=> du/dx = 2x  - 2e²ˣ    -  Cos( eˣ. ln x )(  1/x +  ln x)eˣ

du/dx = 2x  - 2e²ˣ    -  Cos( eˣ. ln x )(  1/x +  ln x)eˣ

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