What is the derivative of 1/((5x^6+4x+1^{9/2)}) ?

The derivative of 1/((5x^6+4x+1^{9/2)}) is -(9(15x^5+2))/((5x^6+4x+1)^{11/2)}

What is the first derivative of 1/((5x^6+4x+1^{9/2)}) ?

The first derivative of 1/((5x^6+4x+1^{9/2)}) is -(9(15x^5+2))/((5x^6+4x+1)^{11/2)}

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}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{9}{2}}})

- \frac{9 ( 15 x ^{5} + 2 )}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{9}{2}}})

Apply exponent rule:

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

= \frac{d}{d x} ((5 x^{6} + 4 x + 1)^{- \frac{9}{2}})

Apply the chain rule:

- \frac{9}{2 ( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}} \frac{d}{d x} (5 x^{6} + 4 x + 1)

= - \frac{9}{2 ( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}} \frac{d}{d x} (5 x^{6} + 4 x + 1)

\frac{d}{d x} (5 x^{6} + 4 x + 1) = 30 x^{5} + 4

= - \frac{9}{2 ( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}} (30 x^{5} + 4)

Simplify

- \frac{9}{2 ( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}} (30 x^{5} + 4) : - \frac{9 ( 15 x ^{5} + 2 )}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}}

= - \frac{9 ( 15 x ^{5} + 2 )}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{11}{2}}}

\frac{d y}{d x} + \frac{6}{x} y = - 5 x + 9

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

\int \frac{x ^{2} + 4 x}{x ^{3} + 6 x ^{2} + 5} d x

\int \frac{x + 1}{x ^{3} - x} d x

\frac{\partial}{\partial L} (K (α) (α)^{α} L^{1 - α})

What is the derivative of 1/((5x^6+4x+1^{9/2)}) ?
The derivative of 1/((5x^6+4x+1^{9/2)}) is -(9(15x^5+2))/((5x^6+4x+1)^{11/2)}
What is the first derivative of 1/((5x^6+4x+1^{9/2)}) ?
The first derivative of 1/((5x^6+4x+1^{9/2)}) is -(9(15x^5+2))/((5x^6+4x+1)^{11/2)}