SOLUTION: If f(x) = 10x^(ln(x)), find f'(2)

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Question 1200748: If f(x) = 10x^(ln(x)), find f'(2)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

+f%28x%29+=+10x%5E%28ln%28x%29%29

ln%28%22f%28x%29%22%5E%22%22%29=ln%2810x%5E%28ln%28x%29%29%29

ln%28%22f%28x%29%22%5E%22%22%29=ln%2810%29%2Bln%28x%5E%28ln%28x%29%29%29

ln%28%22f%28x%29%22%5E%22%22%29=ln%2810%29%2Bln%28x%29%2Aln%28x%29%29

ln%28%22f%28x%29%22%5E%22%22%29=ln%2810%29%2B%28ln%28x%29%29%5E2%29

ln(10) is a constant so its derivative is 0.

%22f%27%28x%29%22%2F%22f%28x%29%22=2%2Aln%28x%29%2Aexpr%281%2Fx%29%29

%22f%27%28x%29%22=%22f%28x%29%22%2A2%2Aln%28x%29%2Aexpr%281%2Fx%29%29

Substitute original expression for f(x)

%22f%27%28x%29%22=10x%5E%28ln%28x%29%29%2A2%2Aln%28x%29%2Aexpr%281%2Fx%29%29

%22f%27%28x%29%22=20x%5E%28ln%28x%29%29%2Aln%28x%29%2Aexpr%281%2Fx%29%29

%22f%27%282%29%22=20%282%29%5E%28ln%282%29%29%2Aln%282%29%2Aexpr%281%2F2%29%29



%22f%27%282%29%22=10%282%29%5E%28ln%282%29%29%2Aln%282%29%29

Edwin