What is the derivative of (8x)/(sqrt(x^2+3)) ?

The derivative of (8x)/(sqrt(x^2+3)) is (24)/((x^2+3)sqrt(x^2+3))

What is the first derivative of (8x)/(sqrt(x^2+3)) ?

The first derivative of (8x)/(sqrt(x^2+3)) is (24)/((x^2+3)sqrt(x^2+3))

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derivative of

\frac{8 x}{x ^{2} + 3}

\frac{24}{( x ^{2} + 3 ) x ^{2} + 3}

Solution steps

\frac{d}{d x} (\frac{8 x}{x ^{2} + 3})

Take the constant out:

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

= 8 \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}}

= 8 \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}

= 8 \cdot \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}}

Simplify

8 \cdot \frac{1 \cdot x ^{2} + 3 - \frac{x}{x ^{2} + 3} x}{( x ^{2} + 3 ) ^{2}} : \frac{24}{( x ^{2} + 3 ) x ^{2} + 3}

= \frac{24}{( x ^{2} + 3 ) x ^{2} + 3}

n = 0 \sum \infty (\frac{1}{7})^{n}

\frac{\partial}{\partial x} (\frac{3 x}{5 y})

(6 x^{2} y^{2}) d x + (4 x^{3} y) d y = 0

\frac{d y}{d x} = \frac{9 x}{cos ( y )}

\int_{0}^{\frac{3 π}{2}} cos^{3} (13 x) d x

What is the derivative of (8x)/(sqrt(x^2+3)) ?
The derivative of (8x)/(sqrt(x^2+3)) is (24)/((x^2+3)sqrt(x^2+3))
What is the first derivative of (8x)/(sqrt(x^2+3)) ?
The first derivative of (8x)/(sqrt(x^2+3)) is (24)/((x^2+3)sqrt(x^2+3))