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

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

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

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

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{x - 3}{2 x + 1})^{4})

\frac{4 ( x - 3 ) ^{3} ( x + 4 )}{( 2 x + 1 ) ^{\frac{5}{2}} 2 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

4 (\frac{x - 3}{2 x + 1})^{3} \frac{x + 4}{( 2 x + 1 ) 2 x + 1} : \frac{4 ( x - 3 ) ^{3} ( x + 4 )}{( 2 x + 1 ) ^{\frac{5}{2}} 2 x + 1}

= \frac{4 ( x - 3 ) ^{3} ( x + 4 )}{( 2 x + 1 ) ^{\frac{5}{2}} 2 x + 1}

\int_{12}^{13} x x^{2} - 144 d x

\frac{\partial}{\partial x} (x y - ln (x y))

\frac{d}{d x} (\frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )})

\int_{- 3}^{0} 1 + 9 - x^{2} d x

\frac{200}{( s + 10 ) ( s + 100 )}

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