What is the derivative of (sqrt(x+5)/(sqrt(x+2))) ?

The derivative of (sqrt(x+5)/(sqrt(x+2))) is -3/(2sqrt(x+5)(x+2)^{3/2)}

What is the first derivative of (sqrt(x+5)/(sqrt(x+2))) ?

The first derivative of (sqrt(x+5)/(sqrt(x+2))) is -3/(2sqrt(x+5)(x+2)^{3/2)}

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\frac{d}{d x} (\frac{x + 5}{x + 2})

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

Solution steps

\frac{d}{d x} (\frac{x + 5}{x + 2})

Simplify

\frac{x + 5}{x + 2} : \frac{x + 5}{x + 2}

= \frac{d}{d x} (\frac{x + 5}{x + 2})

Apply the chain rule:

\frac{1}{2 \frac{x + 5}{x + 2}} \frac{d}{d x} (\frac{x + 5}{x + 2})

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

\frac{d}{d x} (\frac{x + 5}{x + 2}) = - \frac{3}{( x + 2 ) ^{2}}

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

Simplify

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

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

x y^{^{'}} + 2 y = e^{(2 x^{2})}

\frac{\partial}{\partial x} (x \cdot arcsin (\frac{y}{x}))

\frac{10}{( s + 4 ) ( s + 2 ) ^{3}}

\int cos^{2} (2 x + 1) d x

\frac{\partial}{\partial x} (- 2 tan (x) sin (2 y))

What is the derivative of (sqrt(x+5)/(sqrt(x+2))) ?
The derivative of (sqrt(x+5)/(sqrt(x+2))) is -3/(2sqrt(x+5)(x+2)^{3/2)}
What is the first derivative of (sqrt(x+5)/(sqrt(x+2))) ?
The first derivative of (sqrt(x+5)/(sqrt(x+2))) is -3/(2sqrt(x+5)(x+2)^{3/2)}