Y= sin (2x^2 - 3e^x) Find dy/dx?

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Answer 1 · 2018-04-28T07:50:12

#dy/dx= cos(2x^2-3e^x) * (4x-3e^x)#

#y=sin (2x^2 - 3e^x)#

#dy/dx= cos(2x^2-3e^x) * (4x-3e^x)#

Answer 2 · 2018-04-28T08:03:28

#(dy)/(dx)=(4x-3e^x)cos(2x^2-3e^x)#

Here,

#y= sin (2x^2 - 3e^x)#

Let, #u=2x^2-3e^x =>(du)/(dx)=4x-3e^x#

#and y=sinu=>(dy)/(du)=cosu#

#"Using "color(blue)"Chain Rule"#

#color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx).#

#=>(dy)/(dx)=cosuxx(4x-3e^x),where, u=2x^2-3e^x#

#=>(dy)/(dx)=cos(2x^2-3e^x)xx(4x-3e^x)#

#=>(dy)/(dx)=(4x-3e^x)cos(2x^2-3e^x)#