What is the derivative of (3x+1^{-1}) ?

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

What is the first derivative of (3x+1^{-1}) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{- 5 x}{1 - x}

\frac{d}{d x} (a t^{m} + b t^{m + n})

\frac{d}{d x} (sin (x) sin (3 x))

4 x^{2} - 2 x + 4

\frac{\partial}{\partial x} (3 x^{2} + 6 x y^{3})

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