Question 4

Question 1

Differentiate the function:

\(f(x)=({\var{a2}x^{\var{a3}}+\var{a4}})^\var{a1}\)

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\(f(x)=({\var{a2}x^{\var{a3}}+\var{a4}})^\var{a1}\)

Recall the chain rule: \(\frac{df}{dx}=\frac{df}{du}.\frac{du}{dx}\)

let \(u=\var{a2}x^{\var{a3}}+\var{a4}\) then \(f(x)=u^\var{a1}\)

\(\frac{df}{du}=\var{a1}u^{\var{a1}-1}\) and \(\frac{du}{dx}=\var{a3}\times\var{a2}x^{\var{a3}-1}\)

\(\frac{df}{dx}=\var{a1}u^{\simplify{{a1}-1}}.\simplify{{a2}*{a3}x^{{a3}-1}}\)

\(\frac{df}{dx}=\simplify{{a1}*{a2}*{a3}x^{{a3}-1}}({\var{a2}x^{\var{a3}}+\var{a4}})^{\simplify{{a1}-1}}\)

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