What is the derivative of sqrt((3x+7/(5+2x))) ?

The derivative of sqrt((3x+7/(5+2x))) is 1/(2sqrt(3x+7)(2x+5)^{3/2)}

What is the first derivative of sqrt((3x+7/(5+2x))) ?

The first derivative of sqrt((3x+7/(5+2x))) is 1/(2sqrt(3x+7)(2x+5)^{3/2)}

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\frac{d}{d x} (\frac{3 x + 7}{5 + 2 x})

\frac{1}{2 3 x + 7 ( 2 x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{3 x + 7}{5 + 2 x})

Apply the chain rule:

\frac{1}{2 \frac{3 x + 7}{5 + 2 x}} \frac{d}{d x} (\frac{3 x + 7}{5 + 2 x})

= \frac{1}{2 \frac{3 x + 7}{5 + 2 x}} \frac{d}{d x} (\frac{3 x + 7}{5 + 2 x})

\frac{d}{d x} (\frac{3 x + 7}{5 + 2 x}) = \frac{1}{( 5 + 2 x ) ^{2}}

= \frac{1}{2 \frac{3 x + 7}{5 + 2 x}} \cdot \frac{1}{( 5 + 2 x ) ^{2}}

Simplify

\frac{1}{2 \frac{3 x + 7}{5 + 2 x}} \cdot \frac{1}{( 5 + 2 x ) ^{2}} : \frac{1}{2 3 x + 7 ( 2 x + 5 ) ^{\frac{3}{2}}}

= \frac{1}{2 3 x + 7 ( 2 x + 5 ) ^{\frac{3}{2}}}

\frac{d}{d x} ((ln (x + 1))^{2} - e^{x^{2}})

\int ∣ 4 y + 1 ∣ d y

y^{^{'}} + 7 y = t + e^{- 6 t}

2 x d x + d y = 0

n = 0 \sum \infty 5 (0.7)^{n - 1}

What is the derivative of sqrt((3x+7/(5+2x))) ?
The derivative of sqrt((3x+7/(5+2x))) is 1/(2sqrt(3x+7)(2x+5)^{3/2)}
What is the first derivative of sqrt((3x+7/(5+2x))) ?
The first derivative of sqrt((3x+7/(5+2x))) is 1/(2sqrt(3x+7)(2x+5)^{3/2)}