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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

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

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

Simplify

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

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