What is the derivative of (3e^x/(5e^x+4)) ?

The derivative of (3e^x/(5e^x+4)) is (12e^x)/((5e^x+4)^2)

What is the first derivative of (3e^x/(5e^x+4)) ?

The first derivative of (3e^x/(5e^x+4)) is (12e^x)/((5e^x+4)^2)

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\frac{d}{d x} (\frac{3 e ^{x}}{5 e ^{x} + 4})

\frac{12 e ^{x}}{( 5 e ^{x} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 e ^{x}}{5 e ^{x} + 4})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{e ^{x}}{5 e ^{x} + 4})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( e ^{x} ) ( 5 e ^{x} + 4 ) - \frac{d}{d x} ( 5 e ^{x} + 4 ) e ^{x}}{( 5 e ^{x} + 4 ) ^{2}}

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

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

= 3 \cdot \frac{e ^{x} ( 5 e ^{x} + 4 ) - 5 e ^{x} e ^{x}}{( 5 e ^{x} + 4 ) ^{2}}

Simplify

3 \cdot \frac{e ^{x} ( 5 e ^{x} + 4 ) - 5 e ^{x} e ^{x}}{( 5 e ^{x} + 4 ) ^{2}} : \frac{12 e ^{x}}{( 5 e ^{x} + 4 ) ^{2}}

= \frac{12 e ^{x}}{( 5 e ^{x} + 4 ) ^{2}}

t an g e n t f (x) = - \frac{3}{x ^{2} - 4}, (1, 1)

\frac{d}{d x} (ln (1 + ln (x)))

\int (\frac{1}{x \cdot ( 5 - x )}) d x

x \to 0 + lim (1 + csc (x))

\frac{d}{d x} (3 sin (x) - 4 cos (x))

What is the derivative of (3e^x/(5e^x+4)) ?
The derivative of (3e^x/(5e^x+4)) is (12e^x)/((5e^x+4)^2)
What is the first derivative of (3e^x/(5e^x+4)) ?
The first derivative of (3e^x/(5e^x+4)) is (12e^x)/((5e^x+4)^2)