What is d/(dd)((ax+b)/(cx+d)) ?

The solution to d/(dd)((ax+b)/(cx+d)) is (ax+b)/(d(cx+d))

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simplify d/(dd)((ax+b)/(cx+d))

simplify

\frac{d}{dd} (\frac{a x + b}{c x + d})

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

Solution steps

\frac{d}{dd} (\frac{a x + b}{c x + d})

Apply rule:

(a) = a

(\frac{a x + b}{c x + d}) = \frac{a x + b}{c x + d}

= \frac{d}{dd} \cdot \frac{a x + b}{c x + d}

Cancel

\frac{d}{dd} : \frac{1}{d}

= \frac{1}{d} \cdot \frac{a x + b}{c x + d}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot ( a x + b )}{d ( c x + d )}

Apply rule:

1 \cdot a = a

1 \cdot (a x + b) = (a x + b)

= \frac{a x + b}{d ( c x + d )}

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

\int \frac{2}{X} d X

f (x) = 5 e^{5 x}

\int \frac{x ^{3}}{x ^{3} - 1} d x

What is d/(dd)((ax+b)/(cx+d)) ?
The solution to d/(dd)((ax+b)/(cx+d)) is (ax+b)/(d(cx+d))