What is the d/(dl)(2pisqrt(l/({g)(l))}) ?

The d/(dl)(2pisqrt(l/({g)(l))}) is (pi({g}(l)-l d/(dl)({g}(l)))}{sqrt(l)/g (l)^{3/2)}

What is the first d/(dl)(2pisqrt(l/({g)(l))}) ?

The first d/(dl)(2pisqrt(l/({g)(l))}) is (pi({g}(l)-l d/(dl)({g}(l)))}{sqrt(l)/g (l)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d l} (2 π \frac{l}{g ( l )})

\frac{π ( g ( l ) - l \frac{d}{d l} ( g ( l ) ) )}{l g ( l ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d l} (2 π \frac{l}{g ( l )})

Take the constant out:

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

= 2 π \frac{d}{d l} (\frac{l}{g ( l )})

Apply the chain rule:

\frac{1}{2 \frac{l}{g ( l )}} \frac{d}{d l} (\frac{l}{g ( l )})

= \frac{1}{2 \frac{l}{g ( l )}} \frac{d}{d l} (\frac{l}{g ( l )})

\frac{d}{d l} (\frac{l}{g ( l )}) = \frac{g ( l ) - l \frac{d}{d l} ( g ( l ) )}{g ( l ) ^{2}}

= 2 π \frac{1}{2 \frac{l}{g ( l )}} \cdot \frac{g ( l ) - l \frac{d}{d l} ( g ( l ) )}{g ( l ) ^{2}}

Simplify

2 π \frac{1}{2 \frac{l}{g ( l )}} \cdot \frac{g ( l ) - l \frac{d}{d l} ( g ( l ) )}{g ( l ) ^{2}} : \frac{π ( g ( l ) - l \frac{d}{d l} ( g ( l ) ) )}{l g ( l ) ^{\frac{3}{2}}}

= \frac{π ( g ( l ) - l \frac{d}{d l} ( g ( l ) ) )}{l g ( l ) ^{\frac{3}{2}}}

\int \frac{x ^{2} + x - 2}{x ^{4} + 5 x ^{2} + 4} d x

\frac{d}{d x} ((3 + tan (x))^{x})

\frac{\partial}{\partial x} (\frac{( t - y )}{8 t + 3 y})

y^{^{''}} = 1 - 2 y^{^{'}}

5 t

What is the d/(dl)(2pisqrt(l/({g)(l))}) ?
The d/(dl)(2pisqrt(l/({g)(l))}) is (pi({g}(l)-l d/(dl)({g}(l)))}{sqrt(l)/g (l)^{3/2)}
What is the first d/(dl)(2pisqrt(l/({g)(l))}) ?
The first d/(dl)(2pisqrt(l/({g)(l))}) is (pi({g}(l)-l d/(dl)({g}(l)))}{sqrt(l)/g (l)^{3/2)}