What is the d/(d{r)}(({r}+1)!2^{{r}}) ?

The d/(d{r)}(({r}+1)!2^{{r}}) is \Gamma({r}+1+1)\digamma({r}+2)*2^{{r}}+2^{{r}}ln(2)({r}+1)!

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

The first d/(d{r)}(({r}+1)!2^{{r}}) is \Gamma({r}+1+1)\digamma({r}+2)*2^{{r}}+2^{{r}}ln(2)({r}+1)!

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d r} ((r + 1)! 2^{r})

Γ (r + 1 + 1) ϝ (r + 2) \cdot 2^{r} + 2^{r} ln (2) (r + 1)!

Solution steps

\frac{d}{d r} ((r + 1)! \cdot 2^{r})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (r + 1)!, g = 2^{r}

= \frac{d}{d r} ((r + 1)!) 2^{r} + \frac{d}{d r} (2^{r}) (r + 1)!

\frac{d}{d r} ((r + 1)!) = Γ (r + 1 + 1) ϝ (r + 2)

\frac{d}{d r} (2^{r}) = 2^{r} ln (2)

= Γ (r + 1 + 1) ϝ (r + 2) \cdot 2^{r} + 2^{r} ln (2) (r + 1)!

y = \frac{1}{x + 3}

(1 + x^{2})^{3}

sin^{22} (x)

\frac{1500}{x}

y = \frac{1}{2 x}

What is the d/(d{r)}(({r}+1)!2^{{r}}) ?
The d/(d{r)}(({r}+1)!2^{{r}}) is \Gamma({r}+1+1)\digamma({r}+2)*2^{{r}}+2^{{r}}ln(2)({r}+1)!
What is the first d/(d{r)}(({r}+1)!2^{{r}}) ?
The first d/(d{r)}(({r}+1)!2^{{r}}) is \Gamma({r}+1+1)\digamma({r}+2)*2^{{r}}+2^{{r}}ln(2)({r}+1)!