3.10: Homework- Quotient Rule
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Find the derivatives of the following functions.
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\(f(x) = \frac{e^x}{x}\)
\(f'(x) = \frac{x e^x - e^x}{x^2}\)ans
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\(g(x) = \frac{\sqrt[3]{x}}{\ln(x)}\)
ans
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\(h(x) = \frac{1}{x^2 + 5x + 6}\)
\(h'(x) = \frac{-(2x + 5)}{(x^2 + 5x + 6)^2}\)ans
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\(i(x) = \frac{\cos(x)}{1 + x^2}\)
\(i'(x) = \frac{-(1 + x^2) \sin(x) - 2x \cos(x)}{(1 + x^2)^2}\)ans
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\(j(x) = \frac{\ln(x)}{x^2}\)
\(j'(x) = \frac{1 - 2 \ln(x) }{x^3}\)ans
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\(k(x) = e^{-x}\) (How can you write this as a fraction?)
\(k'(x) = \frac{-e^x}{(e^x)^2} = -\frac{1}{e^x}\)ans
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\(\ell(x) = \frac{x e^x}{1 + x}\)
\(\ell'(x) = \frac{x^2 e^x + x e^x + e^x}{(1+x)^2}\)ans
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\(f(x) = \frac{e^x}{x}\)