What is the derivative of ((e^x))/((e^x+4)(x+5)) ?

The derivative of ((e^x))/((e^x+4)(x+5)) is (4e^xx-e^{2x}+16e^x)/((e^x+4)^2(x+5)^2)

What is the first derivative of ((e^x))/((e^x+4)(x+5)) ?

The first derivative of ((e^x))/((e^x+4)(x+5)) is (4e^xx-e^{2x}+16e^x)/((e^x+4)^2(x+5)^2)

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derivative of

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

\frac{4 e ^{x} x - e ^{2 x} + 16 e ^{x}}{( e ^{x} + 4 ) ^{2} ( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{( e ^{x} + 4 ) ( x + 5 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( e ^{x} + 4 ) ( x + 5 ) - \frac{d}{d x} ( ( e ^{x} + 4 ) ( x + 5 ) ) e ^{x}}{( ( e ^{x} + 4 ) ( x + 5 ) ) ^{2}}

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

\frac{d}{d x} ((e^{x} + 4) (x + 5)) = e^{x} x + 6 e^{x} + 4

= \frac{e ^{x} ( e ^{x} + 4 ) ( x + 5 ) - ( e ^{x} x + 6 e ^{x} + 4 ) e ^{x}}{( ( e ^{x} + 4 ) ( x + 5 ) ) ^{2}}

Simplify

\frac{e ^{x} ( e ^{x} + 4 ) ( x + 5 ) - ( e ^{x} x + 6 e ^{x} + 4 ) e ^{x}}{( ( e ^{x} + 4 ) ( x + 5 ) ) ^{2}} : \frac{4 e ^{x} x - e ^{2 x} + 16 e ^{x}}{( e ^{x} + 4 ) ^{2} ( x + 5 ) ^{2}}

= \frac{4 e ^{x} x - e ^{2 x} + 16 e ^{x}}{( e ^{x} + 4 ) ^{2} ( x + 5 ) ^{2}}

csc (y) d x + sec (2) (x) d y = 0

\frac{d ^{2}}{d x ^{2}} (\frac{6 x ^{5}}{5} - 7 x)

\int (sin (y) cos (x)) d x

y^{^{'}} = y^{2} e^{(2 x)}

\frac{d}{d x} (4^{x} ln (x))

What is the derivative of ((e^x))/((e^x+4)(x+5)) ?
The derivative of ((e^x))/((e^x+4)(x+5)) is (4e^xx-e^{2x}+16e^x)/((e^x+4)^2(x+5)^2)
What is the first derivative of ((e^x))/((e^x+4)(x+5)) ?
The first derivative of ((e^x))/((e^x+4)(x+5)) is (4e^xx-e^{2x}+16e^x)/((e^x+4)^2(x+5)^2)