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

The derivative of ((8x)/(sqrt(x^2+4))) is (32)/((x^2+4)sqrt(x^2+4))

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

The first derivative of ((8x)/(sqrt(x^2+4))) is (32)/((x^2+4)sqrt(x^2+4))

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\frac{d}{d x} (\frac{( 8 x )}{x ^{2} + 4})

\frac{32}{( x ^{2} + 4 ) x ^{2} + 4}

Solution steps

\frac{d}{d x} (\frac{( 8 x )}{x ^{2} + 4})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{x}{x ^{2} + 4})

Apply the Quotient Rule:

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

= 8 \cdot \frac{\frac{d x}{d x} x ^{2} + 4 - \frac{d}{d x} ( x ^{2} + 4 ) x}{( x ^{2} + 4 ) ^{2}}

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

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

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

Simplify

8 \cdot \frac{1 \cdot x ^{2} + 4 - \frac{x}{x ^{2} + 4} x}{( x ^{2} + 4 ) ^{2}} : \frac{32}{( x ^{2} + 4 ) x ^{2} + 4}

= \frac{32}{( x ^{2} + 4 ) x ^{2} + 4}

x \to 0 lim (\frac{1 - e ^{x}}{x})

f (x) = 1 - 3 x^{[2]}, at x = 0

\int \frac{3}{y} d y

\int_{1}^{3} \frac{2 x ^{2} + 3 x - 2}{x} d x

\frac{\partial}{\partial s} (\frac{s}{t})

What is the derivative of ((8x)/(sqrt(x^2+4))) ?
The derivative of ((8x)/(sqrt(x^2+4))) is (32)/((x^2+4)sqrt(x^2+4))
What is the first derivative of ((8x)/(sqrt(x^2+4))) ?
The first derivative of ((8x)/(sqrt(x^2+4))) is (32)/((x^2+4)sqrt(x^2+4))