en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)= 1/(1+x)

Solution

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

Solution

y = ln (1 + x) + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

If

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

then

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

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

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

y = ln (1 + x) + c_{1}

Graph

Popular Examples

integral of sqrt(2m(E-1/2 kx^2))

\int 2 m (E - \frac{1}{2} k x^{2}) d x

derivative of f(x)=-12x^2+400x-3800 derivative of

f (x) = - 12 x^{2} + 400 x - 3800

tangent of 3x-4x^2 tangent of

3 x - 4 x^{2}

integral of (1-sin^2(x))cos(x)

\int (1 - sin^{2} (x)) cos (x) d x

derivative of (x^5-5/(x+1))

\frac{d}{d x} (\frac{x ^{5} - 5}{x + 1})

Frequently Asked Questions (FAQ)

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