What is the d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) ?

The d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) is (2({r}^2-1)^2(3{r}+{r}^2+5))/((2{r)+1)^6}

What is the first d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) ?

The first d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) is (2({r}^2-1)^2(3{r}+{r}^2+5))/((2{r)+1)^6}

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\frac{d}{d r} (\frac{( r ^{2} - 1 ) ^{3}}{( 2 r + 1 ) ^{5}})

\frac{2 ( r ^{2} - 1 ) ^{2} ( 3 r + r ^{2} + 5 )}{( 2 r + 1 ) ^{6}}

Solution steps

\frac{d}{d r} (\frac{( r ^{2} - 1 ) ^{3}}{( 2 r + 1 ) ^{5}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d r} ( ( r ^{2} - 1 ) ^{3} ) ( 2 r + 1 ) ^{5} - \frac{d}{d r} ( ( 2 r + 1 ) ^{5} ) ( r ^{2} - 1 ) ^{3}}{( ( 2 r + 1 ) ^{5} ) ^{2}}

\frac{d}{d r} ((r^{2} - 1)^{3}) = 6 r (r^{2} - 1)^{2}

\frac{d}{d r} ((2 r + 1)^{5}) = 10 (2 r + 1)^{4}

= \frac{6 r ( r ^{2} - 1 ) ^{2} ( 2 r + 1 ) ^{5} - 10 ( 2 r + 1 ) ^{4} ( r ^{2} - 1 ) ^{3}}{( ( 2 r + 1 ) ^{5} ) ^{2}}

Simplify

\frac{6 r ( r ^{2} - 1 ) ^{2} ( 2 r + 1 ) ^{5} - 10 ( 2 r + 1 ) ^{4} ( r ^{2} - 1 ) ^{3}}{( ( 2 r + 1 ) ^{5} ) ^{2}} : \frac{2 ( r ^{2} - 1 ) ^{2} ( 3 r + r ^{2} + 5 )}{( 2 r + 1 ) ^{6}}

= \frac{2 ( r ^{2} - 1 ) ^{2} ( 3 r + r ^{2} + 5 )}{( 2 r + 1 ) ^{6}}

\int_{4}^{6} (x^{2} + 2 x - 8) d x

\int x^{3} e^{- \frac{x ^{2}}{2}} d x

\int \frac{25}{x} d x

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

\int \frac{1}{121 - x ^{2}} d x

What is the d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) ?
The d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) is (2({r}^2-1)^2(3{r}+{r}^2+5))/((2{r)+1)^6}
What is the first d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) ?
The first d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5}) is (2({r}^2-1)^2(3{r}+{r}^2+5))/((2{r)+1)^6}