Page:Calculus Made Easy.pdf/47

${\displaystyle y+dy=(x+dx)^{3}+5}$

${\displaystyle =x^{3}+3x^{2}dx+3x(dx)^{2}+(dx)^{3}+5}$.

${\displaystyle y+dy=x^{3}+3x^{2}\cdot dx+5}$.

${\displaystyle dy=3x^{2}dx}$.

${\displaystyle {\frac {dy}{dx}}=3x^{2}}$.

${\displaystyle y+dy=7(x+dx)^{2}}$

${\displaystyle =7\{x^{2}+2x\cdot dx+(dx)^{2}\}}$

${\displaystyle =7x^{2}+14x\cdot dx+7(dx)^{2}}$.

${\displaystyle dy=14x\cdot dx}$.

${\displaystyle {\frac {dy}{dx}}=14x}$.