What is the d/(da)((pi(9a^2-1))/(54a^2)) ?

The d/(da)((pi(9a^2-1))/(54a^2)) is pi/(27a^3)

What is the first d/(da)((pi(9a^2-1))/(54a^2)) ?

The first d/(da)((pi(9a^2-1))/(54a^2)) is pi/(27a^3)

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\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

\frac{π}{27 a ^{3}}

Solution steps

\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

Take the constant out:

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

= \frac{π}{54} \frac{d}{d a} (\frac{9 a ^{2} - 1}{a ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{π}{54} \cdot \frac{\frac{d}{d a} ( 9 a ^{2} - 1 ) a ^{2} - \frac{d}{d a} ( a ^{2} ) ( 9 a ^{2} - 1 )}{( a ^{2} ) ^{2}}

\frac{d}{d a} (9 a^{2} - 1) = 18 a

\frac{d}{d a} (a^{2}) = 2 a

= \frac{π}{54} \cdot \frac{18 a a ^{2} - 2 a ( 9 a ^{2} - 1 )}{( a ^{2} ) ^{2}}

Simplify

\frac{π}{54} \cdot \frac{18 a a ^{2} - 2 a ( 9 a ^{2} - 1 )}{( a ^{2} ) ^{2}} : \frac{π}{27 a ^{3}}

= \frac{π}{27 a ^{3}}

\frac{\partial}{\partial x} (5)

\frac{d y}{d x} - \frac{( y ^{2} - x ^{2} )}{3 x y} = 0

\int 3 x^{4} + 2 x^{2} - \frac{x}{2} d x

\int_{0}^{- 0.6} 150 x d x

x \to - 2 lim ((x^{2} + 5))

What is the d/(da)((pi(9a^2-1))/(54a^2)) ?
The d/(da)((pi(9a^2-1))/(54a^2)) is pi/(27a^3)
What is the first d/(da)((pi(9a^2-1))/(54a^2)) ?
The first d/(da)((pi(9a^2-1))/(54a^2)) is pi/(27a^3)