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some calc questions
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<blockquote data-quote="swimfreak26" data-source="post: 1300634" data-attributes="member: 544365"><p>Just follow the chain rule very closely and you'll be able to do these things after a little effort.</p><p></p><p>The example of ln(x^2):</p><p></p><p>The derivitive is the derivitive of the inside multiplied by the derivitive of the function itself. Now, you know the deriv of ln(u) = u, and the derivitive of x^n = nx^(n-1).</p><p></p><p>So...</p><p></p><p>d/dx (ln(x^2)) = d/dx(x^2) * d/dx(ln(u)) where u is the quantity x^2</p><p></p><p>This gives you:</p><p></p><p>d/dx (ln(x^2)) = 2x/x^2 = 2/x</p><p></p><p>Now, follow the same set of rules for ln(x)^2, where now x is the quantity of "ln(x)" when doing the simple power rule.</p><p></p><p>So you get:</p><p></p><p>d/dx (ln(x)^2)) = (2)(ln(x))(1/x) = 2ln(x)/x</p><p></p><p>Don't know if that helps or not, but I hope so.</p></blockquote><p></p>
[QUOTE="swimfreak26, post: 1300634, member: 544365"] Just follow the chain rule very closely and you'll be able to do these things after a little effort. The example of ln(x^2): The derivitive is the derivitive of the inside multiplied by the derivitive of the function itself. Now, you know the deriv of ln(u) = u, and the derivitive of x^n = nx^(n-1). So... d/dx (ln(x^2)) = d/dx(x^2) * d/dx(ln(u)) where u is the quantity x^2 This gives you: d/dx (ln(x^2)) = 2x/x^2 = 2/x Now, follow the same set of rules for ln(x)^2, where now x is the quantity of "ln(x)" when doing the simple power rule. So you get: d/dx (ln(x)^2)) = (2)(ln(x))(1/x) = 2ln(x)/x Don't know if that helps or not, but I hope so. [/QUOTE]
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