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

The derivative of (cos(x)/(x^2+1)) is (-sin(x)(x^2+1)-2xcos(x))/((x^2+1)^2)

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

The first derivative of (cos(x)/(x^2+1)) is (-sin(x)(x^2+1)-2xcos(x))/((x^2+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

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

Simplify

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

o 2 x 2 - 3 x + 2

\frac{\partial}{\partial y} (2 yz)

\int \frac{x ^{2} + 2 x - 3}{x + 1} d x

\int \frac{6}{6 x - 5} d x

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