Mathematics, 26.11.2020 01:50 parmer6527p810bw
Consider the function f(x) for which f(e)=7 and f'(e)=6 find h'(e) for the function h(x)=f(x)^x h'(e)=
Answers: 3
![h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e]](/tpl/images/0929/5208/e7391.png)
, the first derivative of the function is found by applying the concept of implicit differentiation:
![h'(x) = h(x) \cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right]](/tpl/images/0929/5208/01bdb.png)
![h'(x) = f(x)^{x}\cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right]](/tpl/images/0929/5208/121c6.png)
![h'(x) = f(x)^{x-1}\cdot [f(x)\cdot \ln f(x)+x\cdot f'(x)]](/tpl/images/0929/5208/8bea7.png)
(2)
, 
and 
, then 
is:
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Consider the function f(x) for which f(e)=7 and f'(e)=6 find h'(e) for the function h(x)=f(x)^x
h'(...
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