What is the derivative of (x+1/(2-x)) ?

The derivative of (x+1/(2-x)) is 3/((2-x)^2)

What is the first derivative of (x+1/(2-x)) ?

The first derivative of (x+1/(2-x)) is 3/((2-x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 1) = 1

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

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

Simplify

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

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

u^{'} (x)

e^{c o s (3 x)}

x \to - 3 lim (- \frac{3}{x + 3})

x^{4}

y^{^{''}} + 4 y^{^{'}} - y = 0

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