What is the derivative of y=(3+x^2)^{1/2} ?

The derivative of y=(3+x^2)^{1/2} is x/((3+x^2)^{1/2)}

What is the first derivative of y=(3+x^2)^{1/2} ?

The first derivative of y=(3+x^2)^{1/2} is x/((3+x^2)^{1/2)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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cos (x) - sin (2 x)

7 x^{3} + sin (x) + x^{2} e^{2}

x^{3} + 2 x^{2} + 4

3 x^{4} + 6 x^{2} + 8

What is the derivative of y=(3+x^2)^{1/2} ?
The derivative of y=(3+x^2)^{1/2} is x/((3+x^2)^{1/2)}
What is the first derivative of y=(3+x^2)^{1/2} ?
The first derivative of y=(3+x^2)^{1/2} is x/((3+x^2)^{1/2)}