What is the derivative of 2/(2x+e^{2x}) ?

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

What is the first derivative of 2/(2x+e^{2x}) ?

The first derivative of 2/(2x+e^{2x}) is -(2(2+2e^{2x}))/((2x+e^{2x))^2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} + 2 y^{^{'}} = 3 + 4 sin (2 x)

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

\frac{d}{d x} (\frac{x ^{2} - 8 x + 15}{x ^{2} + 3 x + 2})

(x + a)^{4} (x - a)^{3}

f (x) = x e^{x^{2}}

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