What is the derivative of 2/((6x^2+5x+1)^2) ?

The derivative of 2/((6x^2+5x+1)^2) is -(4(12x+5))/((6x^2+5x+1)^3)

What is the first derivative of 2/((6x^2+5x+1)^2) ?

The first derivative of 2/((6x^2+5x+1)^2) is -(4(12x+5))/((6x^2+5x+1)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}}

- \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{( 6 x ^{2} + 5 x + 1 ) ^{2}})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((6 x^{2} + 5 x + 1)^{- 2})

Apply the chain rule:

- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} \frac{d}{d x} (6 x^{2} + 5 x + 1)

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

\frac{d}{d x} (6 x^{2} + 5 x + 1) = 12 x + 5

= 2 (- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} (12 x + 5))

Simplify

2 (- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} (12 x + 5)) : - \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

= - \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

\int \frac{1}{aa uu} d u

\frac{d}{d x} (\frac{1}{sin ( x ^{2} )})

\int e^{4 x} cos (3 x) d x

\frac{\partial}{\partial x} (y + e^{x})

\int_{0}^{1} \frac{2 x}{1 + x ^{4}} d x

What is the derivative of 2/((6x^2+5x+1)^2) ?
The derivative of 2/((6x^2+5x+1)^2) is -(4(12x+5))/((6x^2+5x+1)^3)
What is the first derivative of 2/((6x^2+5x+1)^2) ?
The first derivative of 2/((6x^2+5x+1)^2) is -(4(12x+5))/((6x^2+5x+1)^3)