What is the derivative of (4x/(sqrt(x^2+2))) ?

The derivative of (4x/(sqrt(x^2+2))) is 8/((x^2+2)sqrt(x^2+2))

What is the first derivative of (4x/(sqrt(x^2+2))) ?

The first derivative of (4x/(sqrt(x^2+2))) is 8/((x^2+2)sqrt(x^2+2))

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\frac{d}{d x} (\frac{4 x}{x ^{2} + 2})

\frac{8}{( x ^{2} + 2 ) x ^{2} + 2}

Solution steps

\frac{d}{d x} (\frac{4 x}{x ^{2} + 2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{x ^{2} + 2})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} x ^{2} + 2 - \frac{d}{d x} ( x ^{2} + 2 ) x}{( x ^{2} + 2 ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot x ^{2} + 2 - \frac{x}{x ^{2} + 2} x}{( x ^{2} + 2 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot x ^{2} + 2 - \frac{x}{x ^{2} + 2} x}{( x ^{2} + 2 ) ^{2}} : \frac{8}{( x ^{2} + 2 ) x ^{2} + 2}

= \frac{8}{( x ^{2} + 2 ) x ^{2} + 2}

\frac{\partial}{\partial x} (x y - z^{2})

\int (8 - \frac{( 5 ^{x} )}{2}) d x

\int \frac{z ( 1 - z )}{( z + 1 ) ( z ^{2} + 1 ) ^{2}} d z

\int t^{2} t^{3} - 1 d t

\int_{0}^{π} sin (x) cos^{2} (x) d x

What is the derivative of (4x/(sqrt(x^2+2))) ?
The derivative of (4x/(sqrt(x^2+2))) is 8/((x^2+2)sqrt(x^2+2))
What is the first derivative of (4x/(sqrt(x^2+2))) ?
The first derivative of (4x/(sqrt(x^2+2))) is 8/((x^2+2)sqrt(x^2+2))