What is (\partial)/(\partial x)(sqrt((x+4)/(x+5))) ?

The answer to (\partial)/(\partial x)(sqrt((x+4)/(x+5))) is 1/(2sqrt(x+4)(x+5)^{3/2)}

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(\partial)/(\partial x)(sqrt((x+4)/(x+5)))

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

\frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

Apply the chain rule:

\frac{1}{2 \frac{x + 4}{x + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

= \frac{1}{2 \frac{x + 4}{x + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5}) = \frac{1}{( x + 5 ) ^{2}}

= \frac{1}{2 \frac{x + 4}{x + 5}} \cdot \frac{1}{( x + 5 ) ^{2}}

Simplify

\frac{1}{2 \frac{x + 4}{x + 5}} \cdot \frac{1}{( x + 5 ) ^{2}} : \frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

= \frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (sin (\frac{y}{x}))

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

(3 x^{2} + 2 x), at (a = - 3)

y = x, y = x - 2, [0, 4]

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} - 3 z^{2} - 11)

What is (\partial)/(\partial x)(sqrt((x+4)/(x+5))) ?
The answer to (\partial)/(\partial x)(sqrt((x+4)/(x+5))) is 1/(2sqrt(x+4)(x+5)^{3/2)}