{"version":8,"graph":{"viewport":{"xmin":-9.111469996126138,"ymin":-9.727131674824214,"xmax":17.26781497753987,"ymax":8.529551463256393}},"randomSeed":"c4402be35e564c7dbcb57ee25509ee99","expressions":{"list":[{"type":"expression","id":"103","color":"#2d70b3","latex":"f\\left(x\\right)=0.4x^{3}-15x","hidden":true},{"type":"expression","id":"104","color":"#388c46","latex":"g\\left(x\\right)=2x+1","hidden":true},{"type":"expression","id":"105","color":"#c74440","latex":"\\frac{f\\left(x\\right)}{g\\left(x\\right)}"},{"type":"text","id":"112","text":"All of the following five expressions are equivalent"},{"type":"expression","id":"107","color":"#2d70b3","latex":"f\\left(x\\right)\\cdot\\frac{d}{dx}\\left(\\frac{1}{g\\left(x\\right)}\\right)+\\frac{1}{g\\left(x\\right)}\\cdot\\frac{d}{dx}f\\left(x\\right)"},{"type":"expression","id":"108","color":"#388c46","latex":"f\\left(x\\right)\\cdot-\\frac{\\frac{d}{dx}g\\left(x\\right)}{g\\left(x\\right)^{2}}+\\frac{1}{g\\left(x\\right)}\\cdot\\frac{d}{dx}f\\left(x\\right)"},{"type":"text","id":"114","text":"The following two (not the third) are totally identical except that the first uses d/dx notation and the second uses apostrophes"},{"type":"expression","id":"109","color":"#fa7e19","latex":"-\\frac{f\\left(x\\right)\\cdot\\frac{d}{dx}g\\left(x\\right)}{g\\left(x\\right)^{2}}+\\frac{\\frac{d}{dx}f\\left(x\\right)}{g\\left(x\\right)}"},{"type":"expression","id":"110","color":"#6042a6","latex":"-\\frac{f\\left(x\\right)g'\\left(x\\right)}{g\\left(x\\right)^{2}}+\\frac{f'\\left(x\\right)}{g\\left(x\\right)}"},{"type":"expression","id":"106","color":"#000000","latex":"\\frac{d}{dx}\\left(\\frac{f\\left(x\\right)}{g\\left(x\\right)}\\right)"}]}}