What is the derivative of (b/(a+z^2))^4 ?

The derivative of (b/(a+z^2))^4 is -(8b^4z)/((a+z^2)^5)

What is the first derivative of (b/(a+z^2))^4 ?

The first derivative of (b/(a+z^2))^4 is -(8b^4z)/((a+z^2)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

(\frac{b}{a + z ^{2}})^{4}

- \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

Solution steps

\frac{d}{d z} ((\frac{b}{a + z ^{2}})^{4})

Apply the chain rule:

4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

= 4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

\frac{d}{d z} (\frac{b}{a + z ^{2}}) = - \frac{2 b z}{( a + z ^{2} ) ^{2}}

= 4 (\frac{b}{a + z ^{2}})^{3} (- \frac{2 b z}{( a + z ^{2} ) ^{2}})

Simplify

4 (\frac{b}{a + z ^{2}})^{3} (- \frac{2 b z}{( a + z ^{2} ) ^{2}}) : - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

= - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

What is the derivative of (b/(a+z^2))^4 ?
The derivative of (b/(a+z^2))^4 is -(8b^4z)/((a+z^2)^5)
What is the first derivative of (b/(a+z^2))^4 ?
The first derivative of (b/(a+z^2))^4 is -(8b^4z)/((a+z^2)^5)