What is the derivative of (ax/b) ?

The derivative of (ax/b) is a/b

What is the first derivative of (ax/b) ?

The first derivative of (ax/b) is a/b

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

\frac{a}{b}

Solution steps

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

Take the constant out:

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

= \frac{a}{b} \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= \frac{a}{b} \cdot 1

Simplify

= \frac{a}{b}

\int \frac{1}{( 4 - x ^{2} ) ^{3}} d x

y - 1 + x y^{^{'}} = 4 x

- 5 x^{2}

\frac{\partial}{\partial x} (\frac{( x ^{2} )}{y + 1})

\int \frac{y}{( y ^{2} - 1 ) ^{\frac{3}{2}}} d y