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 Pre-Calculus Pre-Calculus Math Forum

 October 5th, 2018, 06:20 AM #1 Newbie   Joined: Oct 2018 From: CA Posts: 1 Thanks: 0 Derivatives help Good morning, I was wondering if someone can give me a clear explanation of how to solve for derivatives? Please somebody help me... also what does it mean to solve for "the first derivative"? f(x)=⅓ x2 +7x - 4 f(x)= 5 x3+3x Thank you! October 5th, 2018, 06:48 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,968 Thanks: 2217 It presumably means that you should find the (first) derivative of each of the given functions of x by using the rules of differentiation, such as the power rule. Thanks from ProofOfALifetime October 5th, 2018, 06:59 AM #3 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 Do you know what a first derivative is? There are two ways to find a first derivative. One is to work from the basic definition by taking the limit of the Newton quotient. This is usually done toward the start of a calculus course when they are trying to get you to understand what a derivative is. The other is to apply a set of general rules. First method. $f(x) = 3x^2 \implies \text { Newton quotient } = \dfrac{f(x + h) - f(x)}{h} =$ $\dfrac{3(x^2 + 2xh + h^2) - 3x^2}{h} = \dfrac{3x^2 + 6hx + 3h^2 - 3x^2}{h} = 6x + 3h^2.$ $\therefore \displaystyle \left ( \lim_{h \rightarrow 0} 6x + 3h \right ) = 6x = f'(x).$ Second method is to apply general rules. $\alpha (x) = k * \beta(x), \text { where } k \text { is a constant } \implies \alpha '(x) = k * \beta '(x).$ $\gamma (x) = x^n \implies \gamma '(x) = n * x^{(n-1)}.$ Put those two rules together and you get $f(x) = 3x^2 \implies f'(x) = 3 * ( 2 * x^{(2-1)}) = 6x.$ Thanks from ProofOfALifetime and Ljusbi Tags derivatives Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post johngalt47 Calculus 2 November 23rd, 2013 11:44 AM cacophonyjm Calculus 1 March 20th, 2012 11:13 PM takuto Calculus 1 March 13th, 2010 10:54 PM Tartarus Calculus 2 March 9th, 2010 05:54 PM takuto Calculus 1 March 8th, 2010 10:56 PM

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