Differentiation: Basic differentiation True/false Reflect Your Turn 𝑦= 𝑥 2 −3𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −5 𝑑𝑦 𝑑𝑥 = Rule

@mrbartonmaths 𝑦= 𝑥 2 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +3𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −3𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +3𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −3𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +6 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +3𝑥+6 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +3𝑥+5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +2𝑥+5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +𝑥+5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 +𝑥−5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −𝑥−5 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 = 𝑦=2 𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 = 𝑦= 3𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 = 𝑦= 3𝑥 3 −2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 2𝑥 3 −2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 2𝑥 3 +2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 2𝑥 3 +2−5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 2𝑥 3 −5𝑥+2 𝑑𝑦 𝑑𝑥 = 𝑦=2−5𝑥− 2𝑥 3 𝑑𝑦 𝑑𝑥 = @mrbartonmaths

@mrbartonmaths 𝑦= 𝑥 2 𝑑𝑦 𝑑𝑥 =2𝑥 𝑦= 𝑥 2 +3𝑥 𝑑𝑦 𝑑𝑥 =2𝑥+3 𝑦= 𝑥 2 𝑑𝑦 𝑑𝑥 =2𝑥 𝑦= 𝑥 2 +3𝑥 𝑑𝑦 𝑑𝑥 =2𝑥+3 𝑦= 𝑥 2 −3𝑥 𝑑𝑦 𝑑𝑥 =2𝑥−3 𝑦= 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 =2𝑥−5 𝑦= 𝑥 2 −5 𝑑𝑦 𝑑𝑥 =2𝑥 𝑦= 𝑥 2 +5 𝑑𝑦 𝑑𝑥 =2𝑥 𝑦= 𝑥 2 +6 𝑑𝑦 𝑑𝑥 =2𝑥 𝑦= 𝑥 2 +3𝑥+6 𝑑𝑦 𝑑𝑥 =2𝑥+3 𝑦= 𝑥 2 +3𝑥+5 𝑑𝑦 𝑑𝑥 =2𝑥+3 𝑦= 𝑥 2 +2𝑥+5 𝑑𝑦 𝑑𝑥 =2𝑥+2 𝑦= 𝑥 2 +𝑥+5 𝑑𝑦 𝑑𝑥 =2𝑥+1 𝑦= 𝑥 2 +𝑥−5 𝑑𝑦 𝑑𝑥 =2𝑥+1 𝑦= 𝑥 2 −𝑥−5 𝑑𝑦 𝑑𝑥 =2𝑥−1 𝑦= 𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 =2𝑥−2 𝑦=2 𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 =4𝑥−2 𝑦= 3𝑥 2 −2𝑥−5 𝑑𝑦 𝑑𝑥 =6𝑥−2 𝑦= 3𝑥 3 −2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 9𝑥 2 −4𝑥−5 𝑦= 2𝑥 3 −2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 6𝑥 2 −4𝑥−5 𝑦= 2𝑥 3 +2 𝑥 2 −5𝑥 𝑑𝑦 𝑑𝑥 = 6𝑥 2 +4𝑥−5 𝑦= 2𝑥 3 +2−5𝑥 𝑑𝑦 𝑑𝑥 = 6𝑥 2 −5 𝑦= 2𝑥 3 −5𝑥+2 𝑑𝑦 𝑑𝑥 = 6𝑥 2 −5 𝑦=2−5𝑥− 2𝑥 3 𝑑𝑦 𝑑𝑥 = −5−6𝑥 2 @mrbartonmaths

Your Turn 𝑦= 𝑥 3 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 −5 𝑥 2 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 −5 𝑥 2 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 −5𝑥 𝑑𝑦 𝑑𝑥 = 𝑦= 𝑥 3 −5 𝑑𝑦 𝑑𝑥 = 𝑦= 5−𝑥 3 𝑑𝑦 𝑑𝑥 = @mrbartonmaths

Your Turn - answers 𝑦= 𝑥 3 𝑑𝑦 𝑑𝑥 = 3𝑥 2 𝑦= 𝑥 3 𝑑𝑦 𝑑𝑥 = 3𝑥 2 𝑦= 𝑥 3 −5 𝑥 2 𝑑𝑦 𝑑𝑥 = 3𝑥 2 −10𝑥 𝑦= 𝑥 3 −5𝑥 𝑑𝑦 𝑑𝑥 = 3𝑥 2 −5 𝑦= 𝑥 3 −5 𝑑𝑦 𝑑𝑥 = 3𝑥 2 𝑦= 5−𝑥 3 𝑑𝑦 𝑑𝑥 = −3𝑥 2 @mrbartonmaths