How would I figure out the following question.
Find $f''(x)$ if $f(x)=(x^2-6x-7)^{11}$
Using the chain rule I got the first derivative as.
$11(x^2-6x-7)^{10}(2x-6)$
Applying both the chain rule and the product rule I got
for my second derivative
$f''(x)=11(x^2-6x-7)^{10}(2)+(2x-6)(110)(x^2-6x-7)^9(2x-6)$
However did I do this correctly?
Best Answer
Yes, your answer is correct.
Alternatively you could write $x^2-6x-7=(x+1)(x-7)$ so you can differentiate twice: $$(x+1)^{11}(x-7)^{11}$$
using just the product rule.