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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 4) = 1

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

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

Simplify

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

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

\int_{- 2 π}^{- π} sin^{2} (x) d x

x \to 3 lim (h (x))

y = 8 e x cos (x)

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

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

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