What is the derivative of (4e^x/((4-3e^x)^2)) ?

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

What is the first derivative of (4e^x/((4-3e^x)^2)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{4 e ^{x}}{( 4 - 3 e ^{x} ) ^{2}})

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

Solution steps

\frac{d}{d x} (\frac{4 e ^{x}}{( 4 - 3 e ^{x} ) ^{2}})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((4 - 3 e^{x})^{2}) = - 6 e^{x} (4 - 3 e^{x})

= 4 \cdot \frac{e ^{x} ( 4 - 3 e ^{x} ) ^{2} - ( - 6 e ^{x} ( 4 - 3 e ^{x} ) ) e ^{x}}{( ( 4 - 3 e ^{x} ) ^{2} ) ^{2}}

Simplify

4 \cdot \frac{e ^{x} ( 4 - 3 e ^{x} ) ^{2} - ( - 6 e ^{x} ( 4 - 3 e ^{x} ) ) e ^{x}}{( ( 4 - 3 e ^{x} ) ^{2} ) ^{2}} : \frac{4 e ^{x} ( 3 e ^{x} + 4 )}{( 4 - 3 e ^{x} ) ^{3}}

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

y^{^{'}} - y^{2} - 1 = 0, y (0) = 1

\int 7 sec^{6} (t) d t

\frac{d y}{d x}, x = y e^{y}

n = 1 \sum \infty 3 (- \frac{2}{3})^{n}

\frac{d y}{d x} = \frac{2 + y ^{2}}{2 x y}, y (1) = 1

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