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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{1}{2 x ^{2}})

\frac{d ^{2}}{d x ^{2}} (cos^{2} (3 π x))

\int x^{28} e^{x^{29}} d x

\int ln (\frac{1 - x}{1 + x}) d x

\frac{d ^{2}}{d x ^{2}} (3 e^{- x^{2}})

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