What is the derivative of 1/(((b/2+x^2+a^2)^{3/2)}) ?

The derivative of 1/(((b/2+x^2+a^2)^{3/2)}) is -(48(2x+b))/(((2x+b)^2+4a^2)^{5/2)}

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

The first derivative of 1/(((b/2+x^2+a^2)^{3/2)}) is -(48(2x+b))/(((2x+b)^2+4a^2)^{5/2)}

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}{( ( \frac{b}{2} + x ) ^{2} + a ^{2} ) ^{\frac{3}{2}}}

- \frac{48 ( 2 x + b )}{( ( 2 x + b ) ^{2} + 4 a ^{2} ) ^{\frac{5}{2}}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{3}{2 ( ( \frac{b}{2} + x ) ^{2} + a ^{2} ) ^{\frac{5}{2}}} (2 x + b) : - \frac{48 ( 2 x + b )}{( ( 2 x + b ) ^{2} + 4 a ^{2} ) ^{\frac{5}{2}}}

= - \frac{48 ( 2 x + b )}{( ( 2 x + b ) ^{2} + 4 a ^{2} ) ^{\frac{5}{2}}}

\int e^{x} 45 + e^{x} d x

x d y = 8 y d x

\int \frac{2 x y ^{5}}{9 + x ^{2} y ^{2} - y ^{4}} d x

x \to 9 - lim (\frac{- 7}{( x + 9 )})

x \to 0 lim (8 sin (x) ln (x))

What is the derivative of 1/(((b/2+x^2+a^2)^{3/2)}) ?
The derivative of 1/(((b/2+x^2+a^2)^{3/2)}) is -(48(2x+b))/(((2x+b)^2+4a^2)^{5/2)}
What is the first derivative of 1/(((b/2+x^2+a^2)^{3/2)}) ?
The first derivative of 1/(((b/2+x^2+a^2)^{3/2)}) is -(48(2x+b))/(((2x+b)^2+4a^2)^{5/2)}