What is the derivative of 2pisqrt(l/({g(x))}) ?

The derivative of 2pisqrt(l/({g(x))}) is -(pisqrt(l) derivative of {g}(x))/({g)(x)^{3/2}}

What is the first derivative of 2pisqrt(l/({g(x))}) ?

The first derivative of 2pisqrt(l/({g(x))}) is -(pisqrt(l) derivative of {g}(x))/({g)(x)^{3/2}}

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\frac{d}{d x} (2 π \frac{l}{g ( x )})

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

Solution steps

\frac{d}{d x} (2 π \frac{l}{g ( x )})

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (1 + cot^{2} (θ)) (csc^{2} (θ)) d θ

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

y^{^{''}} - y^{^{'}} + 9 y = 3 sin (3 t)

x \to + 2 lim (\frac{1}{2})

\frac{d}{d t} (t^{2} t)

What is the derivative of 2pisqrt(l/({g(x))}) ?
The derivative of 2pisqrt(l/({g(x))}) is -(pisqrt(l) derivative of {g}(x))/({g)(x)^{3/2}}
What is the first derivative of 2pisqrt(l/({g(x))}) ?
The first derivative of 2pisqrt(l/({g(x))}) is -(pisqrt(l) derivative of {g}(x))/({g)(x)^{3/2}}