Quotient rule calculus proof1/7/2024 ![]() ![]() lim - x)(x+h) - (x) - lim 0 vxh)(x) h-0 h Recall that the limit of a difference is the difference of the limits.Use this to separate the expression into two limits. Recall that the limit of a product is the product of the limits. f(x) Tim hVx+x) HỆ 7 x + ) - VA | - vịw up x + h) - HỆx || Click to select your answer 20 888 $ # 3 A 2 4 5 6 & 7 Q W E R T Y uk A S D F G H 7įollowing the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. F(x) = lim vuxh) - xvxh) - vx) h-x+h) x) h 1 O c. (x) - lim himno vpx + hyv(x) * "* Factor out (x) and (x). hx+h)-[ xxl Click to select your answer OSC 30 FA 17 A 1 & 2 $ 4 3 % 5 6 7 8 W E R T Y U A S D F G I Z х C V B Nįollowing the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. Choose the correct answer below 1 OA (x)= tim h- oh (xh)(x) - UIX+h) h OB (x) lim 1 hvo VỆx + (K) ubxh(x) - x)( xh) th 1 Oc) im. (x) = lim u(x + h)x) - (x)(x+h) h-0 h-v(x +hX Factor out the denominator. ![]() Choose the correct ans O A f'(x) = lim h-fu(x + h)(x) u(x)(x + h) ho VIX+hX) OB. Using the identity = and the rule for dividing fractions, rewrite the limit so that it contains one fraction. 30 Fa 17 A 1 2 3 $ 4 5 09 & 7 8 Q W E R T Y U A S D F G I 7 Cįollowing the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. UX+h)(x) - U(X)x+h) V[x+h) ulxh h- Click to select your answer. VIX+hX) Rewrite the numerator of the limit using the found common denominator Choose the correct answer below. Find a common denominator for the fractions in the numerator. This Question: 1 pt 5 of 16 (3 complete) Following the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. Choose the correct answer below Click to select your answer OSC YO 6 & 1 2 # 3 $ 4 Ол ? 6 7 8 Q W E R T Y U А S D F G H N Х с V B Vix) Rewrite the numerator of the limit using the found common denominator. What is the common denominator? O A vix+hX) OB. VOX) v(x+h) f'(x) = lim h Find a common denominator for the fractions in the numerator. Substitute u(x) for f(x) in the equation. Choose the correct answer below 1 ulxh) +(x) OA 700- EX) h 1 X) 1 vIx+ -X) Click to select your answer S: ! 1 2 $ 4 3 5 6 V2 8 9 ३ E R T Y U А S D F G I Lock N х C V B N alt ntrol option commandįollowing the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. x) lim 11x +h)-f(x) th Substitute ) 1 Vix) for f(x) in the equation. What is the derivative of f(x) look like in limit form? O A f'(x) = Tim h- *x+h)-f(x) h fix) - fix + h) OB fx)= im O c. 1 Letf(x) = Then fix) (x) v(x) v(x) From here, use the proof of the product rule to help prove the quotient rule. ![]() Following the steps used to prove the product rule for derivatives, prove the quotient rule for derivatives. ![]()
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