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

The derivative of 1/((1+x^2sqrt(1+x^2))) is -(3x)/((1+x^2)^{5/2)}

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

The first derivative of 1/((1+x^2sqrt(1+x^2))) is -(3x)/((1+x^2)^{5/2)}

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( ( 1 + x ^{2} ) 1 + x ^{2} ) ^{2}} \cdot 3 x 1 + x^{2} : - \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

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

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

x \to 1 lim (F (x))

\int 2 cos (4 x) e^{s i n (4 x)} d x

2 n d

What is the derivative of 1/((1+x^2sqrt(1+x^2))) ?
The derivative of 1/((1+x^2sqrt(1+x^2))) is -(3x)/((1+x^2)^{5/2)}
What is the first derivative of 1/((1+x^2sqrt(1+x^2))) ?
The first derivative of 1/((1+x^2sqrt(1+x^2))) is -(3x)/((1+x^2)^{5/2)}