What is the derivative of y=(x+1)/((x+2)^2) ?

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

What is the first derivative of y=(x+1)/((x+2)^2) ?

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

(x^{2} + 3)^{4} (x^{2} + 5)^{2}

\frac{d}{d t} (50 + 4 t)

(e^{9 x})^{2}

e^{x} y^{2}

3 - 2 x + 4 x^{2}

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