What is the derivative of (13e^{6x})/(x+5) ?

The derivative of (13e^{6x})/(x+5) is (13(6e^{6x}x+29e^{6x}))/((x+5)^2)

What is the first derivative of (13e^{6x})/(x+5) ?

The first derivative of (13e^{6x})/(x+5) is (13(6e^{6x}x+29e^{6x}))/((x+5)^2)

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derivative of

\frac{13 e ^{6 x}}{x + 5}

\frac{13 ( 6 e ^{6 x} x + 29 e ^{6 x} )}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{13 e ^{6 x}}{x + 5})

Take the constant out:

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

= 13 \frac{d}{d x} (\frac{e ^{6 x}}{x + 5})

Apply the Quotient Rule:

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

= 13 \cdot \frac{\frac{d}{d x} ( e ^{6 x} ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) e ^{6 x}}{( x + 5 ) ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= 13 \cdot \frac{e ^{6 x} \cdot 6 ( x + 5 ) - 1 \cdot e ^{6 x}}{( x + 5 ) ^{2}}

Simplify

13 \cdot \frac{e ^{6 x} \cdot 6 ( x + 5 ) - 1 \cdot e ^{6 x}}{( x + 5 ) ^{2}} : \frac{13 ( 6 e ^{6 x} x + 29 e ^{6 x} )}{( x + 5 ) ^{2}}

= \frac{13 ( 6 e ^{6 x} x + 29 e ^{6 x} )}{( x + 5 ) ^{2}}

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What is the derivative of (13e^{6x})/(x+5) ?
The derivative of (13e^{6x})/(x+5) is (13(6e^{6x}x+29e^{6x}))/((x+5)^2)
What is the first derivative of (13e^{6x})/(x+5) ?
The first derivative of (13e^{6x})/(x+5) is (13(6e^{6x}x+29e^{6x}))/((x+5)^2)