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

The derivative of (x^2/(x^2+x+2)) is (x^2+4x)/((x^2+x+2)^2)

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

The first derivative of (x^2/(x^2+x+2)) is (x^2+4x)/((x^2+x+2)^2)

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

\frac{x ^{2} + 4 x}{( x ^{2} + x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

= \frac{x ^{2} + 4 x}{( x ^{2} + x + 2 ) ^{2}}

\frac{\partial}{\partial y} (e^{x} - 1)

\int (1 - sin^{2} (θ)) d θ

\frac{d}{d x} ((2 x^{2} - 1)^{3} (x^{4} + 3)^{5})

75 (1 - \frac{t}{24})^{2}

\int t sec^{2} (4 t) d t

What is the derivative of (x^2/(x^2+x+2)) ?
The derivative of (x^2/(x^2+x+2)) is (x^2+4x)/((x^2+x+2)^2)
What is the first derivative of (x^2/(x^2+x+2)) ?
The first derivative of (x^2/(x^2+x+2)) is (x^2+4x)/((x^2+x+2)^2)