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

The derivative of (x^2+3x+3)^{-3} is -(3(2x+3))/((x^2+3x+3)^4)

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

The first derivative of (x^2+3x+3)^{-3} is -(3(2x+3))/((x^2+3x+3)^4)

Popular >

derivative of

(x^{2} + 3 x + 3)^{- 3}

- \frac{3 ( 2 x + 3 )}{( x ^{2} + 3 x + 3 ) ^{4}}

Solution steps

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

Apply the chain rule:

- \frac{3}{( x ^{2} + 3 x + 3 ) ^{4}} \frac{d}{d x} (x^{2} + 3 x + 3)

= - \frac{3}{( x ^{2} + 3 x + 3 ) ^{4}} \frac{d}{d x} (x^{2} + 3 x + 3)

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

= - \frac{3}{( x ^{2} + 3 x + 3 ) ^{4}} (2 x + 3)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 ( 2 x + 3 )}{( x ^{2} + 3 x + 3 ) ^{4}}

\frac{e ^{x}}{( e ^{x} + 1 )}

sin^{3} (x) + cos^{2} (x)

y = (x + 1) (x + 2) (x - 3)

4 t^{2} - 15 t + 25

\frac{x ^{4}}{9}

What is the derivative of (x^2+3x+3)^{-3} ?
The derivative of (x^2+3x+3)^{-3} is -(3(2x+3))/((x^2+3x+3)^4)
What is the first derivative of (x^2+3x+3)^{-3} ?
The first derivative of (x^2+3x+3)^{-3} is -(3(2x+3))/((x^2+3x+3)^4)