Differensiasie: Kortpad differensiasie DATABASIS

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$Bepaal space die space eerste space afgeleide space van bold italic f bold left parenthesis bold italic x bold right parenthesis bold equals bold minus bold 5 bold italic x to the power of bold 2 bold plus bold 2 bold italic x$

$f apostrophe left parenthesis x right parenthesis equals negative 10 x to the power of 1 plus 2$

DK_y=-5x^2+2x

$Differensieer space vir space y space as bold italic y bold equals bold italic x to the power of bold 2 bold minus fraction numerator bold 1 over denominator bold 2 bold italic x to the power of bold 3 end fraction$

$fraction numerator d y over denominator d x end fraction equals 2 x plus fraction numerator 3 over denominator 2 x to the power of 4 end fraction$

DKB1_y=x^2-1d(2x^3)

$Differensieer space vir space y space as space bold italic y bold equals bold italic x to the power of bold 2 bold minus bold 1 over bold 2 bold italic x to the power of bold 3$

$fraction numerator d y over denominator d x end fraction equals 2 x plus 3 over 2 x squared$

DK_y=x^2-0.5x^3

$Indien space square root of x equals y to the power of fraction numerator 1 over denominator 3 space end fraction end exponent en space y equals z to the power of negative 3 end exponent space bepaal space fraction numerator d y over denominator d z end fraction$

$fraction numerator d y over denominator d z end fraction equals negative 3 z to the power of negative 4 end exponent$

DK_y=x^-3

$Gebruik space differensiasie space re straight e with ¨ on top ls space en space bepaal fraction numerator d y over denominator d x end fraction space as space bold italic y bold equals begin bold style left parenthesis 2 minus 5 x right parenthesis end style to the power of bold 2$

$fraction numerator d y over denominator d x end fraction equals negative 10 plus 50 x$

DKH_y=(2-5x)^2

$Gebruik space differensiasie space re straight e with ¨ on top ls space en space bepaal space fraction numerator d y over denominator d x end fraction space as bold space bold italic y bold equals bold left parenthesis bold italic x to the power of bold 3 bold plus bold 1 bold right parenthesis bold left parenthesis bold italic x to the power of bold 2 bold minus bold 2 bold right parenthesis$

$fraction numerator d y over denominator d x end fraction equals 5 x to the power of 4 minus 6 x squared plus 2 x$

DKH_y=(x^3+1)(x^2-2)

$Evalueer space bold italic D subscript bold x bold left parenthesis bold x to the power of bold 3 bold minus bold 3 bold right parenthesis to the power of bold 2$

$3 x squared minus 18 x squared$

DKH_y=(x^3-3)^2

$Evalueer space bold italic D subscript bold x begin bold style left square bracket left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis right square bracket end style$

$equals 2 x plus 1$

DKH_y=(x-2)(x+3)

$Bereken space bold italic D subscript bold x begin bold style left square bracket 4 minus 4 over x cubed minus 1 over x to the power of 4 right square bracket end style$

$equals 12 x to the power of negative 4 end exponent plus 4 x to the power of negative 5 end exponent$

DKB1_y=4-4dx^3-1dx^4

$Bepaal space fraction numerator d y over denominator d x end fraction space as space y bold equals fraction numerator bold x to the power of bold 4 bold minus bold 3 bold x to the power of bold 2 bold plus bold 7 over denominator bold x end fraction$

$y apostrophe equals 3 x squared minus 3 minus 7 over x squared$

DKB3_y=(x^4-3x^2+7)dx