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

The derivative of f(x)= 1/(-2+(3x+1)^2) is -(18x+6)/((9x^2+6x-1)^2)

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

The first derivative of f(x)= 1/(-2+(3x+1)^2) is -(18x+6)/((9x^2+6x-1)^2)

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derivative of

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

- \frac{18 x + 6}{( 9 x ^{2} + 6 x - 1 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (- 2 + (3 x + 1)^{2}) = 18 x + 6

= - \frac{1}{( - 2 + ( 3 x + 1 ) ^{2} ) ^{2}} (18 x + 6)

Simplify

- \frac{1}{( - 2 + ( 3 x + 1 ) ^{2} ) ^{2}} (18 x + 6) : - \frac{18 x + 6}{( 9 x ^{2} + 6 x - 1 ) ^{2}}

= - \frac{18 x + 6}{( 9 x ^{2} + 6 x - 1 ) ^{2}}

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

\frac{d}{d x} (sinh^{2} (x))

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

\int \frac{y}{3 y + 1} d y

\frac{d y}{d x} = 3 cos (x) y, y (\frac{π}{2}) = - 2

What is the derivative of f(x)= 1/(-2+(3x+1)^2) ?
The derivative of f(x)= 1/(-2+(3x+1)^2) is -(18x+6)/((9x^2+6x-1)^2)
What is the first derivative of f(x)= 1/(-2+(3x+1)^2) ?
The first derivative of f(x)= 1/(-2+(3x+1)^2) is -(18x+6)/((9x^2+6x-1)^2)