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Question 1150697: Differentiate the following
a) z=3x^2+4x^3
b) f(x)=(x^2+1)(x-5)/x
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) use the power rule
dz/dx = 6x +12x^2
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b) f(x) = (x^2+1)(x-5)/x = (x^3 -5x^2 +x -5)/x = x^2 -5x +1 -5/x
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the last algebra step is the result of distributing x through the expression in parenthesis
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f'(x) = 2x -5 +5/x^2
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Note derivative of -5/x use the quotient rule, that is, derivative of -5/x = 0 -(-5)(1)/x^2 = 5/x^2
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