What is the derivative of (2x/(sqrt(x+20))) ?

The derivative of (2x/(sqrt(x+20))) is (x+40)/((x+20)sqrt(x+20))

What is the first derivative of (2x/(sqrt(x+20))) ?

The first derivative of (2x/(sqrt(x+20))) is (x+40)/((x+20)sqrt(x+20))

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\frac{d}{d x} (\frac{2 x}{x + 20})

\frac{x + 40}{( x + 20 ) x + 20}

Solution steps

\frac{d}{d x} (\frac{2 x}{x + 20})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{x + 20})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} x + 20 - \frac{d}{d x} ( x + 20 ) x}{( x + 20 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x + 20) = \frac{1}{2 x + 20}

= 2 \cdot \frac{1 \cdot x + 20 - \frac{1}{2 x + 20} x}{( x + 20 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot x + 20 - \frac{1}{2 x + 20} x}{( x + 20 ) ^{2}} : \frac{x + 40}{( x + 20 ) x + 20}

= \frac{x + 40}{( x + 20 ) x + 20}

y d y = - x d x

\frac{\partial}{\partial x} (x^{2} - 0.1 \cdot cos (6 \cdot x))

\frac{d y}{d x} = 3 + e^{- 3 x + y + 4}

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

\int_{0}^{1} \frac{1}{t ^{2} + 1} d t

What is the derivative of (2x/(sqrt(x+20))) ?
The derivative of (2x/(sqrt(x+20))) is (x+40)/((x+20)sqrt(x+20))
What is the first derivative of (2x/(sqrt(x+20))) ?
The first derivative of (2x/(sqrt(x+20))) is (x+40)/((x+20)sqrt(x+20))