What is the derivative of (4e^{4x}/(e^8(e^{16)-1)}) ?

The derivative of (4e^{4x}/(e^8(e^{16)-1)}) is (16e^{4x-8})/(e^{16)-1}

What is the first derivative of (4e^{4x}/(e^8(e^{16)-1)}) ?

The first derivative of (4e^{4x}/(e^8(e^{16)-1)}) is (16e^{4x-8})/(e^{16)-1}

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 ^{4 x}}{e ^{8} ( e ^{16} - 1 )})

\frac{16 e ^{4 x - 8}}{e ^{16} - 1}

Solution steps

\frac{d}{d x} (\frac{4 e ^{4 x}}{e ^{8} ( e ^{16} - 1 )})

Take the constant out:

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

= \frac{4}{e ^{8} ( e ^{16} - 1 )} \frac{d}{d x} (e^{4 x})

Apply the chain rule:

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

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

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

= \frac{4}{e ^{8} ( e ^{16} - 1 )} e^{4 x} \cdot 4

Simplify

\frac{4}{e ^{8} ( e ^{16} - 1 )} e^{4 x} \cdot 4 : \frac{16 e ^{4 x - 8}}{e ^{16} - 1}

= \frac{16 e ^{4 x - 8}}{e ^{16} - 1}

y = sin (x), at x = \frac{5 π}{3}

x \to 0 lim (\frac{5 ^{x} - 7 ^{x}}{x})

x \to 0 lim (\frac{x ^{2} - 3}{x})

\frac{d y}{d x} (2) - 4 x y = 8 x

\int 8^{3 x + 1} d x

What is the derivative of (4e^{4x}/(e^8(e^{16)-1)}) ?
The derivative of (4e^{4x}/(e^8(e^{16)-1)}) is (16e^{4x-8})/(e^{16)-1}
What is the first derivative of (4e^{4x}/(e^8(e^{16)-1)}) ?
The first derivative of (4e^{4x}/(e^8(e^{16)-1)}) is (16e^{4x-8})/(e^{16)-1}