What is the derivative of 1/(x^2(3x+1)) ?

The derivative of 1/(x^2(3x+1)) is -(9x+2)/(x^3(3x+1)^2)

What is the first derivative of 1/(x^2(3x+1)) ?

The first derivative of 1/(x^2(3x+1)) is -(9x+2)/(x^3(3x+1)^2)

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

- \frac{9 x + 2}{x ^{3} ( 3 x + 1 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} (3 x + 1)) = 9 x^{2} + 2 x

= - \frac{1}{( x ^{2} ( 3 x + 1 ) ) ^{2}} (9 x^{2} + 2 x)

Simplify

- \frac{1}{( x ^{2} ( 3 x + 1 ) ) ^{2}} (9 x^{2} + 2 x) : - \frac{9 x + 2}{x ^{3} ( 3 x + 1 ) ^{2}}

= - \frac{9 x + 2}{x ^{3} ( 3 x + 1 ) ^{2}}

\frac{\partial}{\partial x} (x y^{2} cos (2 + x^{2} y))

2 sin (x), [0, π]

f (x) = \frac{5}{2 5 x + 6}, at x = 6

\frac{\partial}{\partial x} (3 x)

y^{^{'}} - 4 y = 7 e^{4 x}

What is the derivative of 1/(x^2(3x+1)) ?
The derivative of 1/(x^2(3x+1)) is -(9x+2)/(x^3(3x+1)^2)
What is the first derivative of 1/(x^2(3x+1)) ?
The first derivative of 1/(x^2(3x+1)) is -(9x+2)/(x^3(3x+1)^2)