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Popular >

derivative of y=(ax+b)/(cx+d)

Solution

derivative of

y = \frac{a x + b}{c x + d}

Solution

\frac{- b c + a d}{( c x + d ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( a x + b ) ( c x + d ) - \frac{d}{d x} ( c x + d ) ( a x + b )}{( c x + d ) ^{2}}

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

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

= \frac{a ( c x + d ) - c ( a x + b )}{( c x + d ) ^{2}}

Expand

a (c x + d) - c (a x + b) : - b c + a d

= \frac{- b c + a d}{( c x + d ) ^{2}}

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\frac{d}{d x} (sin (tan (x)))

(\partial)/(\partial x)(z(arctan(y/x)))

\frac{\partial}{\partial x} (z (arctan (\frac{y}{x})))

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Frequently Asked Questions (FAQ)

What is the derivative of y=(ax+b)/(cx+d) ?
The derivative of y=(ax+b)/(cx+d) is (-bc+ad)/((cx+d)^2)
What is the first derivative of y=(ax+b)/(cx+d) ?
The first derivative of y=(ax+b)/(cx+d) is (-bc+ad)/((cx+d)^2)