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

The derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) is -4/((x+1)^3)

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

The first derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) is -4/((x+1)^3)

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derivative of

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

- \frac{4}{( x + 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 2 x + 2 ) ( x ^{2} + 2 x + 1 ) - ( 2 x + 2 ) ( x ^{2} + 2 x + 3 )}{( x ^{2} + 2 x + 1 ) ^{2}} : - \frac{4}{( x + 1 ) ^{3}}

= - \frac{4}{( x + 1 ) ^{3}}

\frac{\partial}{\partial x} (- yz)

y = cos (sin (tan (5 x)))

3^{x^{2} + 1}

\frac{\partial}{\partial x} (x^{a} b^{b})

\int \frac{x}{4 + 9 x ^{2}} d x

What is the derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) ?
The derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) is -4/((x+1)^3)
What is the first derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) ?
The first derivative of f(x)=(x^2+2x+3)/(x^2+2x+1) is -4/((x+1)^3)