Answer to Question #242757 in Calculus for JaytheCreator

Question #242757

Let ð‘“ be a function which is everywhere differentiable and for which ð‘“(2) = −3 and 𑓠′ (ð‘¥) = √𑥠2 + 5. Given that ð‘” is defined such that ð‘”(ð‘¥) = ð‘¥ 2ð‘“ ( 𑥠𑥠− 1 ), show that 𑔠′ (2) = −24.


1
Expert's answer
2021-09-28T00:00:52-0400

Given that "f'(x)=\\sqrt{x^2+5}"


"g(x)=x^2(f(x)-1)"

Differentiating "g(x)" w.r.t ."x," we get:

"g'(x)=2x(f(x)-1)+x^2(f'(x))"

Put "x=2"

"g'(2)=4(f(2)-1)+2^2(f'(2))"

"=4((-3)-1)+4f'(2)\\\\\n=-16+4(3)\\\\\n=-4"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment