en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

xdy=dx

Solution

x d y = d x

Solution

y = ln (x) + c_{1}

Solution steps

x d y = d x

Let

y

be the dependent variable. Divide by

d x

:

x \frac{d y}{d x} = 1

Substitute

\frac{d y}{d x}

with

y^{'} (x)

x y^{^{'}} (x) = 1

Isolate

y^{'} (x) : y^{'} (x) = \frac{1}{x}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{1}{x} d x

\int \frac{1}{x} d x = ln (x) + c_{1}

y = ln (x) + c_{1}

Graph

Popular Examples

derivative of ln(sqrt((1+x/(1-x))))

\frac{d}{d x} (ln (\frac{1 + x}{1 - x}))

derivative of sin(3xy)

\frac{d}{d x} (sin (3 x y))

derivative of y=4sec(5x)

d er i v a t i v e y = 4 sec (5 x)

derivative of sqrt(sin(2x+1))

\frac{d}{d x} (sin (2 x + 1))

tangent of (10x)/(1+x^2)

t an g e n t \frac{10 x}{1 + x ^{2}}

Frequently Asked Questions (FAQ)

What is the solution for xdy=dx ?
The solution for xdy=dx is y=ln(x)+c_{1}