What is the derivative of f(x)=(1-2x)/(3-x) ?

The derivative of f(x)=(1-2x)/(3-x) is -5/((3-x)^2)

What is the first derivative of f(x)=(1-2x)/(3-x) ?

The first derivative of f(x)=(1-2x)/(3-x) is -5/((3-x)^2)

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derivative of

f (x) = \frac{1 - 2 x}{3 - x}

- \frac{5}{( 3 - x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - 2 x) = - 2

\frac{d}{d x} (3 - x) = - 1

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

Simplify

\frac{( - 2 ) ( 3 - x ) - ( - 1 ) ( 1 - 2 x )}{( 3 - x ) ^{2}} : - \frac{5}{( 3 - x ) ^{2}}

= - \frac{5}{( 3 - x ) ^{2}}

\frac{d}{d x} (x + 7)

\int [6 cos (x) - 2 sec (x) tan (x)] d x

\int sec (u) tan (u) d u

x \to 7 + lim (\frac{∣ x - 7 ∣}{x - 7})

lo g_{3} (x^{3} + 1)

What is the derivative of f(x)=(1-2x)/(3-x) ?
The derivative of f(x)=(1-2x)/(3-x) is -5/((3-x)^2)
What is the first derivative of f(x)=(1-2x)/(3-x) ?
The first derivative of f(x)=(1-2x)/(3-x) is -5/((3-x)^2)