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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

x \to + 4 + lim (\frac{3}{x - 4})

\frac{\partial}{\partial x} (- 5 e^{x} \cdot cos (yz))

x \to - 2 lim (x^{3} + 6 x^{2} - 16)

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

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

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