What is the derivative of (sqrt(x)-3/(sqrt(x)+3)) ?

The derivative of (sqrt(x)-3/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}

What is the first derivative of (sqrt(x)-3/(sqrt(x)+3)) ?

The first derivative of (sqrt(x)-3/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}

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\frac{d}{d x} (\frac{x - 3}{x + 3})

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

Solution steps

\frac{d}{d x} (\frac{x - 3}{x + 3})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 3) = \frac{1}{2 x}

\frac{d}{d x} (x + 3) = \frac{1}{2 x}

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

Simplify

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

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

\frac{d}{d x} (\frac{m}{x})

f (t) = \frac{2 t}{t ^{2} + 1}

f (x) = \frac{1}{x ^{2}}, at x = 5

f (x) = 3 x^{2} - 4 x, (1, - 1)

- 3 cos (x)

What is the derivative of (sqrt(x)-3/(sqrt(x)+3)) ?
The derivative of (sqrt(x)-3/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}
What is the first derivative of (sqrt(x)-3/(sqrt(x)+3)) ?
The first derivative of (sqrt(x)-3/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}