en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{y-ln(x})

Solution

\frac{d}{d x} (e^{y - l n (x)})

Solution

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

Solution steps

\frac{d}{d x} (e^{y - l n (x)})

Apply the chain rule:

e^{y - l n (x)} \frac{d}{d x} (y - ln (x))

= e^{y - l n (x)} \frac{d}{d x} (y - ln (x))

\frac{d}{d x} (y - ln (x)) = \frac{d y}{d x} - \frac{1}{x}

= e^{y - l n (x)} (\frac{d y}{d x} - \frac{1}{x})

Simplify

e^{y - l n (x)} (\frac{d y}{d x} - \frac{1}{x}) : \frac{e ^{y} ( x \frac{d y}{d x} - 1 )}{x ^{2}}

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

Popular Examples

derivative of (x^4/(sqrt(x^5+3)))

\frac{d}{d x} (\frac{x ^{4}}{x ^{5} + 3})

(\partial)/(\partial y)(3x+y)

\frac{\partial}{\partial y} (3 x + y)

integral of (23)/(23+e^x)

\int \frac{23}{23 + e ^{x}} d x

(\partial)/(\partial x)(xy+ln(x+y))

\frac{\partial}{\partial x} (x y + ln (x + y))

derivative of sin^{ln(x}(3x))

\frac{d}{d x} (sin^{l n (x)} (3 x))

Frequently Asked Questions (FAQ)

What is the derivative of e^{y-ln(x}) ?
The derivative of e^{y-ln(x}) is (e^y(x\frac{dy)/(dx)-1)}{x^2}
What is the first derivative of e^{y-ln(x}) ?
The first derivative of e^{y-ln(x}) is (e^y(x\frac{dy)/(dx)-1)}{x^2}