求教一道导数，42题？
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(42)
y=f[(3x-2)/(5x+2)], f'(x) =arctan(x^2)
To find : dy/dx |x=0
soluton :
y=f[(3x-2)/(5x+2)]
dy/dx
= f'[(3x-2)/(5x+2)] . { 16 .[ 1/(5x+2)^2] }
=16 [ 1/(5x+2)^2] . f'[(3x-2)/(5x+2)]
=16 [ 1/(5x+2)^2] . arctan{ [(3x-2)/(5x+2)]^2 }
dy/dx | x=0
=16 (1/4) . arctan(1)
=16 (1/4) (π/4)
=π
y=f[(3x-2)/(5x+2)], f'(x) =arctan(x^2)
To find : dy/dx |x=0
soluton :
y=f[(3x-2)/(5x+2)]
dy/dx
= f'[(3x-2)/(5x+2)] . { 16 .[ 1/(5x+2)^2] }
=16 [ 1/(5x+2)^2] . f'[(3x-2)/(5x+2)]
=16 [ 1/(5x+2)^2] . arctan{ [(3x-2)/(5x+2)]^2 }
dy/dx | x=0
=16 (1/4) . arctan(1)
=16 (1/4) (π/4)
=π
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