What is the derivative of (6x/(sqrt(x^2+3))) ?

The derivative of (6x/(sqrt(x^2+3))) is (18)/((x^2+3)sqrt(x^2+3))

What is the first derivative of (6x/(sqrt(x^2+3))) ?

The first derivative of (6x/(sqrt(x^2+3))) is (18)/((x^2+3)sqrt(x^2+3))

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\frac{d}{d x} (\frac{6 x}{x ^{2} + 3})

\frac{18}{( x ^{2} + 3 ) x ^{2} + 3}

Solution steps

\frac{d}{d x} (\frac{6 x}{x ^{2} + 3})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{x}{x ^{2} + 3})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d x}{d x} x ^{2} + 3 - \frac{d}{d x} ( x ^{2} + 3 ) x}{( x ^{2} + 3 ) ^{2}}

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

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

= 6 \cdot \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}} : \frac{18}{( x ^{2} + 3 ) x ^{2} + 3}

= \frac{18}{( x ^{2} + 3 ) x ^{2} + 3}

\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

\frac{d}{d x} (sec^{2} (3 - 2 x))

x^{2} - 1

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

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

What is the derivative of (6x/(sqrt(x^2+3))) ?
The derivative of (6x/(sqrt(x^2+3))) is (18)/((x^2+3)sqrt(x^2+3))
What is the first derivative of (6x/(sqrt(x^2+3))) ?
The first derivative of (6x/(sqrt(x^2+3))) is (18)/((x^2+3)sqrt(x^2+3))