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Solution assignment 27 Product and Quotient rule

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Assignment 27

Differentiate:

y=\displaystyle\frac{e^{3x}}{x^2+1}

Solution

We have to apply the quotient rule and use the result of the previous assignment:

f'(x)=3e^{3x}

g'(x)=2x

If we apply the product rule we get:

y'=\displaystyle\frac{(x^2+1)\cdot3e^{3x}-e^{3x}\cdot2x}{(x^2+1)^2}=\displaystyle\frac{(3x^2-2x+3)e^{3x}}{(x^2+1)^2}

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