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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d a} (\frac{( 1 + 2 cos ^{2} ( a ) )}{( 1 + 3 cot ^{2} ( a ) )})

\frac{- x ^{4}}{2}

y = x y + 10 x + 10 y

x^{2} + 3 x + 5

x^{2} + 3 x + 7

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