section 2.6: chain rule (homework)\nscore: 150/170 answered: 15/17\nprogress saved done\nquestion 16\n0/10…

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\neq1) 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})