We appreciate your visit to Given a 4 14 f a 3 and the derivative values f a 2 and f a 5 8 find F a for F f. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
F'(a) = 160, is obtained by applying the chain rule to differentiate the given composite function F(x) = f(x^5) with respect to x. The correct option is b) F'(a) = 160.
Explanation:
To find F'(a) for F(x) = f(x5), we use the chain rule. The chain rule in calculus says that if you have two functions u(x) and f(u), the derivative of the composition of these functions, f(u(x)), with respect to x is the product of the derivative of f with respect to u and the derivative of u with respect to x.
To find F'(a) for F = f(x⁵), we need to use the chain rule for derivatives. Given f(a⁴) = 14, f'(a) = 3, f'(a) = 2, and f'(a⁵) = 8, we can substitute into the chain rule formula to get F'(a) = 5a⁴ * f'(a⁵) = 5(14) * 8 = 160.
In our case, u(x) = x5 and f(u) is the given function f. Thus, F'(x) = f'(u(x)) \\* u'(x). We have f'(a5) = 8 and u'(x) = 5x4, hence, u'(a) = 5a4 = 5 \\* 14 = 70. Therefore, F'(a) = f'(a5) \\* u'(a) = 8 \\* 70 = 160.
Thanks for taking the time to read Given a 4 14 f a 3 and the derivative values f a 2 and f a 5 8 find F a for F f. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
