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Can you help me answer these 3 questions please. I'm supposed find their derivatives

Can you help me answer these 3 questions please. I'm supposed find their derivatives-example-1

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4 votes

Answer:


f^(\prime)(x)=(x^2-3)/(x^2)

Step-by-step explanation:

Given the function f(x) defined as follows:


f(x)=(x^2+3)/(x)

We use the quotient rule to differentiate this.


\text{Quotient Rule:}(v(du)/(dx)-u(dv)/(dx))/(v^2)

From f(x):


\begin{gathered} u=x^2+3,(du)/(dx)=2x \\ v=x,(dv)/(dx)=1 \end{gathered}

Therefore:


\begin{gathered} f^(\prime)(x)=(x(2x)-(x^2+3))/(x^2) \\ =(2x^2-x^2-3)/(x^2) \\ f^(\prime)(x)=(x^2-3)/(x^2) \end{gathered}

User Udit Gogoi
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