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3.5, #8, Given Problem.
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Given Problem. |
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We differentiate using the power rule. Because there is an inner function, we use the chain rule. |
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Here the first quantity is squared |
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..and here we do the polynomial multiplication |
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..and here we use the distributive property to arrive at our derivative. |
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Here we first multiply out the original given product, |
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..and then take the derivative. We arrive at the same solution. |
3.5, #16, Given Problem.
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Given Problem. |
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We use the product rule. |
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Simplify |
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Factor. This is our derivative. |
3.5, #34, Given Problem.
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Given Problem. |
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We need the chain rule and the product rule in order to find this first derivative. |
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Now we calculate the second derivative. |
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Now we substitute each of our derivatives into the given differential equation. |
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After simplifying, we have shown that the differential equation is true |
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