Find the following. Explain your answer f'(0) for f(x)=5^(5/3)sgn x

Trystan Castaneda 2022-08-16 Answered
Find the following. Explain your answer
f ( 0 )  for  f ( x ) = x 5 3 s g n   x
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Answers (1)

Kelton Glover
Answered 2022-08-17 Author has 17 answers
Solution: f ( x ) = x 5 3 s g n   x
{ 1 x < 0 0 x = 0 1 x > 0
d d x ( x n ) = n x n 1
Now, f ( x ) = s g n   x d d x ( x 5 3 ) + x 5 3 d d x ( s g n   x ) = s g n   x 5 3 × 1 3 + x 5 3 × 0 f ( 0 ) = 0 + 0 = 0
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