What is the derivative of (6e^x/(5e^x+7)) ?

The derivative of (6e^x/(5e^x+7)) is (42e^x)/((5e^x+7)^2)

What is the first derivative of (6e^x/(5e^x+7)) ?

The first derivative of (6e^x/(5e^x+7)) is (42e^x)/((5e^x+7)^2)

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Popular >

\frac{d}{d x} (\frac{6 e ^{x}}{5 e ^{x} + 7})

\frac{42 e ^{x}}{( 5 e ^{x} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 e ^{x}}{5 e ^{x} + 7})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{e ^{x}}{5 e ^{x} + 7})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d}{d x} ( e ^{x} ) ( 5 e ^{x} + 7 ) - \frac{d}{d x} ( 5 e ^{x} + 7 ) e ^{x}}{( 5 e ^{x} + 7 ) ^{2}}

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

\frac{d}{d x} (5 e^{x} + 7) = 5 e^{x}

= 6 \cdot \frac{e ^{x} ( 5 e ^{x} + 7 ) - 5 e ^{x} e ^{x}}{( 5 e ^{x} + 7 ) ^{2}}

Simplify

6 \cdot \frac{e ^{x} ( 5 e ^{x} + 7 ) - 5 e ^{x} e ^{x}}{( 5 e ^{x} + 7 ) ^{2}} : \frac{42 e ^{x}}{( 5 e ^{x} + 7 ) ^{2}}

= \frac{42 e ^{x}}{( 5 e ^{x} + 7 ) ^{2}}

\frac{d}{d x} (a^{x} + x^{a})

\int_{1}^{4} \frac{2 x + 1}{2 x} d x

\frac{d}{d x} (x + 4)

\frac{\partial}{\partial x} (x arctan (\frac{x}{y}))

x \to \infty lim (x + x^{3})

What is the derivative of (6e^x/(5e^x+7)) ?
The derivative of (6e^x/(5e^x+7)) is (42e^x)/((5e^x+7)^2)
What is the first derivative of (6e^x/(5e^x+7)) ?
The first derivative of (6e^x/(5e^x+7)) is (42e^x)/((5e^x+7)^2)