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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 6) = 1

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

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

Simplify

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

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

\frac{d}{d x} (3 x^{2} - 5 x + 6)

\frac{d y}{d x} = - 8 y

\int 17 x^{16} d x

f (x) = - 3 x + 1

\int \frac{3 x}{3 - x ^{2}} d x

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