图上这题怎么做?
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y=f[(3x-2)/(5x+2)]
f'(x) = arctan(x^2)
dy/dx|x=0 = ?
solution :
y=f[(3x-2)/(5x+2)]
dy/dx
= [16/(5x+2)^2] .f'[(3x-2)/(5x+2)]
= [16/(5x+2)^2] .arctan( [(3x-2)/(5x+2)]^2 )
dy/dx| x=0
= (16/4) .arctan(1)
=4(π/4)
=π
f'(x) = arctan(x^2)
dy/dx|x=0 = ?
solution :
y=f[(3x-2)/(5x+2)]
dy/dx
= [16/(5x+2)^2] .f'[(3x-2)/(5x+2)]
= [16/(5x+2)^2] .arctan( [(3x-2)/(5x+2)]^2 )
dy/dx| x=0
= (16/4) .arctan(1)
=4(π/4)
=π
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