What is the derivative of (a+bx/(c+dx)) ?

The derivative of (a+bx/(c+dx)) is (bc-ad)/((c+dx)^2)

What is the first derivative of (a+bx/(c+dx)) ?

The first derivative of (a+bx/(c+dx)) is (bc-ad)/((c+dx)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

3 t e^{- 2 t}

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

\int \frac{1}{sin ^{4} ( x )} d x

\frac{d}{d x} (z (x) + x^{2})

\int_{0}^{1} t 1 + t^{2} + t^{4} d t

What is the derivative of (a+bx/(c+dx)) ?
The derivative of (a+bx/(c+dx)) is (bc-ad)/((c+dx)^2)
What is the first derivative of (a+bx/(c+dx)) ?
The first derivative of (a+bx/(c+dx)) is (bc-ad)/((c+dx)^2)