What is the derivative of (e^2/(x(3x-5))) ?

The derivative of (e^2/(x(3x-5))) is -(e^2(6x-5))/(x^2(3x-5)^2)

What is the first derivative of (e^2/(x(3x-5))) ?

The first derivative of (e^2/(x(3x-5))) is -(e^2(6x-5))/(x^2(3x-5)^2)

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\frac{d}{d x} (\frac{e ^{2}}{x ( 3 x - 5 )})

- \frac{e ^{2} ( 6 x - 5 )}{x ^{2} ( 3 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{2}}{x ( 3 x - 5 )})

Take the constant out:

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

= e^{2} \frac{d}{d x} (\frac{1}{x ( 3 x - 5 )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= e^{2} \frac{d}{d x} ((x (3 x - 5))^{- 1})

Apply the chain rule:

- \frac{1}{( x ( 3 x - 5 ) ) ^{2}} \frac{d}{d x} (x (3 x - 5))

= - \frac{1}{( x ( 3 x - 5 ) ) ^{2}} \frac{d}{d x} (x (3 x - 5))

\frac{d}{d x} (x (3 x - 5)) = 6 x - 5

= e^{2} (- \frac{1}{( x ( 3 x - 5 ) ) ^{2}} (6 x - 5))

Simplify

e^{2} (- \frac{1}{( x ( 3 x - 5 ) ) ^{2}} (6 x - 5)) : - \frac{e ^{2} ( 6 x - 5 )}{x ^{2} ( 3 x - 5 ) ^{2}}

= - \frac{e ^{2} ( 6 x - 5 )}{x ^{2} ( 3 x - 5 ) ^{2}}

What is the derivative of (e^2/(x(3x-5))) ?
The derivative of (e^2/(x(3x-5))) is -(e^2(6x-5))/(x^2(3x-5)^2)
What is the first derivative of (e^2/(x(3x-5))) ?
The first derivative of (e^2/(x(3x-5))) is -(e^2(6x-5))/(x^2(3x-5)^2)