What is the derivative of (e^{2x+1}/(2x+5)) ?

The derivative of (e^{2x+1}/(2x+5)) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)

What is the first derivative of (e^{2x+1}/(2x+5)) ?

The first derivative of (e^{2x+1}/(2x+5)) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)

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

\frac{4 e ^{2 x + 1} x + 8 e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

e^{2 x + 1} \cdot 2 (2 x + 5) - 2 e^{2 x + 1} : 4 e^{2 x + 1} x + 8 e^{2 x + 1}

= \frac{4 e ^{2 x + 1} x + 8 e ^{2 x + 1}}{( 2 x + 5 ) ^{2}}

n = 1 \sum \infty \frac{ln ( n )}{2 n}

y = \frac{3}{x}, y = 12 x

\frac{\partial}{\partial x} (y^{\frac{z}{x}})

\int \frac{( 8 x - 3 )}{( 4 x ^{2} + ( - 3 ) x )} d x

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

What is the derivative of (e^{2x+1}/(2x+5)) ?
The derivative of (e^{2x+1}/(2x+5)) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)
What is the first derivative of (e^{2x+1}/(2x+5)) ?
The first derivative of (e^{2x+1}/(2x+5)) is (4e^{2x+1}x+8e^{2x+1})/((2x+5)^2)