en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(2^x-4)

Solution

derivative of

ln (2^{x} - 4)

Solution

\frac{ln ( 2 ) \cdot 2 ^{x}}{2 ^{x} - 4}

Solution steps

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

Apply the chain rule:

\frac{1}{2 ^{x} - 4} \frac{d}{d x} (2^{x} - 4)

= \frac{1}{2 ^{x} - 4} \frac{d}{d x} (2^{x} - 4)

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

= \frac{1}{2 ^{x} - 4} ln (2) \cdot 2^{x}

Simplify

\frac{1}{2 ^{x} - 4} ln (2) \cdot 2^{x} : \frac{ln ( 2 ) \cdot 2 ^{x}}{2 ^{x} - 4}

= \frac{ln ( 2 ) \cdot 2 ^{x}}{2 ^{x} - 4}

Popular Examples

(\partial)/(\partial y)(3cos(x)-sin(x)y)

\frac{\partial}{\partial y} (3 cos (x) - sin (x) y)

area y=(25-4x^2)^2,x=-5/2 ,x= 5/2 area

y = (25 - 4 x^{2})^{2}, x = - \frac{5}{2}, x = \frac{5}{2}

integral of (5x+3)/(x^2+1)

\int \frac{5 x + 3}{x ^{2} + 1} d x

sum from n=1 to infinity of 19^nx^nn!

n = 1 \sum \infty 1 9^{n} x^{n} n!

limit as x approaches-2+of (-6x)/(x+2)

x \to - 2 + lim (\frac{- 6 x}{x + 2})

Frequently Asked Questions (FAQ)

What is the derivative of ln(2^x-4) ?
The derivative of ln(2^x-4) is (ln(2)*2^x)/(2^x-4)
What is the first derivative of ln(2^x-4) ?
The first derivative of ln(2^x-4) is (ln(2)*2^x)/(2^x-4)