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

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

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

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

Popular >

derivative of

(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}}}

\frac{- x}{( x - 1 )}

\frac{d}{d x} (cos^{2} (y) - sin^{2} (x))

f (x) = (6 x^{2} + 7 x)^{4}

y = \frac{3 x \cdot 5 + 2}{x}

y = (x^{3} + 3)^{4}

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