Differensiasie: Kortpad differensiasie DATABASIS

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$Bepaal space fraction numerator d y over denominator d x end fraction space as space bold bold 2 bold italic x bold italic y bold equals bold 2 bold italic x to the power of bold 2 bold minus bold 7 bold italic x bold plus bold 6$

$fraction numerator d y over denominator d x end fraction equals 1 minus 3 over x squared$

DKBG_2xy=2x^2-7x+6

$Vir space die space volgende space funksie colon space bold italic f begin bold style left parenthesis x right parenthesis end style bold equals begin bold style left parenthesis 2 x minus 3 right parenthesis end style begin bold style left parenthesis x plus 4 right parenthesis end style bold plus fraction numerator bold 2 over denominator bold 3 bold x to the power of bold 4 end fraction a right parenthesis space space space Bepaal space die space eerste space afgeleide. straight b right parenthesis space space space Bepaal space die space tweede space afgeleide.$

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell 4 x plus 5 minus fraction numerator 8 over denominator 3 x to the power of 5 end fraction end cell row cell f apostrophe apostrophe open parentheses x close parentheses end cell equals cell 4 plus fraction numerator 40 over denominator 3 x to the power of 6 end fraction end cell end table$

DKBH_y=(2x-3)(x+4)+2d3x^4

$text Bepaal end text space bold italic D subscript bold x begin bold style left square bracket 3 x squared plus open parentheses 3 x close parentheses squared plus 3 x to the power of 0 minus k plus m over x right square bracket end style$

$equals 24 x minus m over x squared$

DKBH_y=3x^2+(3x)^2-k+mdx

$Bepaal space die space eerste space afgeleide space van bold italic y bold equals bold 2 bold italic x to the power of bold 2 bold plus square root of bold x to the power of bold 3 end root$

$fraction numerator d y over denominator d x end fraction equals 4 x plus 3 over 2 square root of x$

DKW_y=2x^2+wx^3

$Bepaal space fraction numerator d y over denominator d x end fraction space as bold space bold italic y bold equals fraction numerator square root of bold x bold minus bold 4 over denominator square root of bold x end fraction$

$fraction numerator d y over denominator d x end fraction equals fraction numerator 2 over denominator square root of x cubed end root end fraction$

DKWB_y=(wx-4)dwx

$Evalueer space bold italic D subscript bold t bold space begin bold style left square bracket fraction numerator negative t to the power of 1 half end exponent plus cube root of t squared end root over denominator square root of t end fraction right square bracket end style$

$equals fraction numerator 1 over denominator 6 root index space 6 of x to the power of 5 end root end fraction$

DKWB_y=(-x^0.5+3wx^2)d(wx)

$Bepaal space die space eerste space afgeleide space van bold italic y bold equals fraction numerator bold 2 over denominator bold 5 square root of bold x end fraction bold minus root index bold 3 of bold x$

$y apostrophe equals negative fraction numerator 1 over denominator 5 square root of x cubed end root end fraction minus fraction numerator 1 over denominator 3 cube root of x squared end root end fraction$

DKWB_y=2d(5wx)-3wx

$Differensieer space vir space y space as space bold italic y bold equals fraction numerator bold 4 over denominator square root of bold x end fraction bold minus bold x to the power of bold 3 over bold 9$

$fraction numerator d y over denominator d x end fraction equals fraction numerator negative 2 over denominator square root of x cubed end root end fraction minus x squared over 3$

DKWB_y=4dwx-x^3d9

$Evalueer space bold D subscript bold x begin bold style left square bracket square root of x cubed end root plus fraction numerator 1 over denominator 3 x cubed end fraction right square bracket end style$

$equals fraction numerator 1 over denominator 3 cube root of x squared end root end fraction minus 1 over x to the power of 4$

DKWB_y=wx^3+1d(3x^3)

$Bepaal space fraction numerator d y over denominator d x end fraction space indien bold space bold italic y bold equals fraction numerator square root of bold x over denominator bold 2 end fraction bold minus fraction numerator bold 1 over denominator bold 6 bold x to the power of bold 3 end fraction$

$fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator 4 square root of x end fraction plus fraction numerator 1 over denominator 2 x to the power of 4 end fraction$

DKWB_y=wxd2-1d(6x^3)