Question

section 2.6: chain rule (homework)
score: 150/170 answered: 15/17
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question 16
0/10 pts 4 99 details
differentiate (f(y)=9^{-7y + 4})
(f(y)=)

Explanation:

Step1: Recall chain - rule formula

The chain - rule states that if \(y = a^{u}\), then \(y^\prime=a^{u}\ln a\cdot u^\prime\), where \(a> 0,a
eq1\) and \(u\) is a function of the variable. Here \(a = 9\) and \(u=-7y + 4\).

Step2: Find the derivative of \(u\) with respect to \(y\)

Differentiate \(u=-7y + 4\) with respect to \(y\). Using the power - rule \((x^n)^\prime=nx^{n - 1}\), we have \(u^\prime=\frac{d}{dy}(-7y + 4)=-7\).

Step3: Apply the chain - rule

Since \(f(y)=9^{-7y + 4}\), by the chain - rule \(f^\prime(y)=9^{-7y + 4}\ln9\cdot(-7)\).

Answer:

\(-7\ln9\cdot9^{-7y + 4}\)