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Use the reciprocal rule to determine the derivative of the function…

Use the reciprocal rule to determine the derivative of the function…-example-1
User Pzaenger
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The function is given as,


f(x)=(1)/(5-6x)

Differentiating both sides with respect to 'x',


f^(\prime)(x)=(d)/(dx)((1)/(5-6x))

According to the reciprocal rule,


(d)/(dx)((1)/(g(x)))=(-g^(\prime)(x))/(g(x)^2)

Comparing with the expression,


g(x)=5-6x

The corresponding derivative is given by,


\begin{gathered} g^(\prime)(x)=(d)/(dx)(5-6x) \\ g^(\prime)(x)=(d)/(dx)(5)-6\cdot(d)/(dx)(x) \\ g^(\prime)(x)=0-6(1) \\ g^(\prime)(x)=-6 \end{gathered}

Substitute the values in the formula,


\begin{gathered} (d)/(dx)((1)/(5-6x))=(-(-6))/((5-6x)^2) \\ (d)/(dx)((1)/(5-6x))=(6)/((5-6x)^2) \end{gathered}

So the derivative of the given function becomes,


f^(\prime)(x)=(6)/((5-6x)^2)

Thus, the derivative of the given function is obtained as,


f^(\prime)(x)=(6)/((5-6x)^2)

User Ryan Neuffer
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