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

The derivative of (1+x^2)^{1/2} is x/((1+x^2)^{1/2)}

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

The first derivative of (1+x^2)^{1/2} is x/((1+x^2)^{1/2)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (sin (\frac{x}{( y + 1 )}))

f (x) = 10 x + 52

\frac{d}{d r ( h )} \frac{( ( r ( h ) + h ) ^{4} )}{h ^{4}}

\frac{( x + 2 )}{( y - 2 )}

sin (lo g_{10} (1 + x))

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