What is the derivative of (4x/(sqrt(x^2+6))) ?

The derivative of (4x/(sqrt(x^2+6))) is (24)/((x^2+6)sqrt(x^2+6))

What is the first derivative of (4x/(sqrt(x^2+6))) ?

The first derivative of (4x/(sqrt(x^2+6))) is (24)/((x^2+6)sqrt(x^2+6))

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\frac{d}{d x} (\frac{4 x}{x ^{2} + 6})

\frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

Solution steps

\frac{d}{d x} (\frac{4 x}{x ^{2} + 6})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x}{x ^{2} + 6})

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} + 6 - \frac{d}{d x} ( x ^{2} + 6 ) x}{( x ^{2} + 6 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 6) = \frac{x}{x ^{2} + 6}

= 4 \cdot \frac{1 \cdot x ^{2} + 6 - \frac{x}{x ^{2} + 6} x}{( x ^{2} + 6 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot x ^{2} + 6 - \frac{x}{x ^{2} + 6} x}{( x ^{2} + 6 ) ^{2}} : \frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

= \frac{24}{( x ^{2} + 6 ) x ^{2} + 6}

y d x - (4 x^{2} y + x) d y = 0

\frac{d}{d x} (ln (x e^{- 7 x}))

\int_{1.5}^{2.5} 9800 (7 - y) (1) d y

\frac{1}{s ^{2} + 16}

\frac{1}{s ( s ^{2} + s + \frac{5}{4} )}

What is the derivative of (4x/(sqrt(x^2+6))) ?
The derivative of (4x/(sqrt(x^2+6))) is (24)/((x^2+6)sqrt(x^2+6))
What is the first derivative of (4x/(sqrt(x^2+6))) ?
The first derivative of (4x/(sqrt(x^2+6))) is (24)/((x^2+6)sqrt(x^2+6))