What is the derivative of 1/((-x^2+3x+3^4)) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{1}{( - x ^{2} + 3 x + 3 ) ^{4}})

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

Solution steps

\frac{d}{d x} (\frac{1}{( - x ^{2} + 3 x + 3 ) ^{4}})

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{4}{( - x ^{2} + 3 x + 3 ) ^{5}} \frac{d}{d x} (- x^{2} + 3 x + 3)

= - \frac{4}{( - x ^{2} + 3 x + 3 ) ^{5}} \frac{d}{d x} (- x^{2} + 3 x + 3)

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

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

Multiply fractions:

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

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

x \to 3 + lim (\frac{3 x}{x - 3})

x \to 1 lim (\frac{x ^{m} - 1}{x - 1})

f (x) = \frac{x ^{2}}{x - 3}, at x = 0

\frac{\partial}{\partial x} (cos (x + 9 y))

y d y = x d x

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