What is the derivative of b/x ?

The derivative of b/x is -b/(x^2)

What is the first derivative of b/x ?

The first derivative of b/x is -b/(x^2)

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\frac{d}{d x} (\frac{b}{x})

- \frac{b}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{b}{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= b \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= b \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= b (- 1 \cdot x^{- 1 - 1})

Simplify

b (- 1 \cdot x^{- 1 - 1}) : - \frac{b}{x ^{2}}

= - \frac{b}{x ^{2}}

\frac{d y}{d x} = \frac{x ^{2} y ^{2}}{1 + x}

\int_{0}^{5} 2 x^{2} e^{- x} d x

3500 (1 - \frac{1}{50} t)^{2}

3 t (2 t^{2} - 5)^{4}

\frac{( s - 2 )}{( s - 2 ) ^{2} + 1}