What is the derivative of (3e^x)/(2e^x-7) ?

The derivative of (3e^x)/(2e^x-7) is -(21e^x)/((2e^x-7)^2)

What is the first derivative of (3e^x)/(2e^x-7) ?

The first derivative of (3e^x)/(2e^x-7) is -(21e^x)/((2e^x-7)^2)

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derivative of

\frac{3 e ^{x}}{2 e ^{x} - 7}

- \frac{21 e ^{x}}{( 2 e ^{x} - 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 e ^{x}}{2 e ^{x} - 7})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{e ^{x}}{2 e ^{x} - 7})

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

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

\frac{d}{d x} (2 e^{x} - 7) = 2 e^{x}

= 3 \cdot \frac{e ^{x} ( 2 e ^{x} - 7 ) - 2 e ^{x} e ^{x}}{( 2 e ^{x} - 7 ) ^{2}}

Simplify

3 \cdot \frac{e ^{x} ( 2 e ^{x} - 7 ) - 2 e ^{x} e ^{x}}{( 2 e ^{x} - 7 ) ^{2}} : - \frac{21 e ^{x}}{( 2 e ^{x} - 7 ) ^{2}}

= - \frac{21 e ^{x}}{( 2 e ^{x} - 7 ) ^{2}}

\int 7 sin^{2} (x co) s^{2} x d x

\frac{\partial}{\partial x} (2 x (5 y - 6))

x \to 6 + lim (\frac{9 x}{x - 6})

f (x) = 3 x^{3} x

x y^{^{'}} + 6 y = x^{3} - x

What is the derivative of (3e^x)/(2e^x-7) ?
The derivative of (3e^x)/(2e^x-7) is -(21e^x)/((2e^x-7)^2)
What is the first derivative of (3e^x)/(2e^x-7) ?
The first derivative of (3e^x)/(2e^x-7) is -(21e^x)/((2e^x-7)^2)