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

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

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

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

Solution steps

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

Simplify

\frac{x - 3}{x + 3} : \frac{x - 3}{x + 3}

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{x - 3}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}}

Simplify

\frac{1}{2 \frac{x - 3}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}} : \frac{3}{x - 3 ( x + 3 ) ^{\frac{3}{2}}}

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

x^{2} + 7

\int x^{2} 2 x - 1 d x

\frac{d x}{d t} + t^{7} x^{9} + \frac{x}{t} = 0

\frac{d ^{2}}{d x ^{2}} (cos (sin (3 θ)))

f (x) = - \frac{24}{( 4 x + 1 )}, at x = - 1

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