What is the derivative of 1000(1+r/(12))^{60} ?

The derivative of 1000(1+r/(12))^{60} is 5000(r/(12)+1)^{59}

What is the first derivative of 1000(1+r/(12))^{60} ?

The first derivative of 1000(1+r/(12))^{60} is 5000(r/(12)+1)^{59}

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derivative of

1000 (1 + \frac{r}{12})^{60}

5000 (\frac{r}{12} + 1)^{59}

Solution steps

\frac{d}{d r} (1000 (1 + \frac{r}{12})^{60})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 1000 \frac{d}{d r} ((1 + \frac{r}{12})^{60})

Apply the chain rule:

60 (1 + \frac{r}{12})^{59} \frac{d}{d r} (1 + \frac{r}{12})

= 60 (1 + \frac{r}{12})^{59} \frac{d}{d r} (1 + \frac{r}{12})

\frac{d}{d r} (1 + \frac{r}{12}) = \frac{1}{12}

= 1000 \cdot 60 (1 + \frac{r}{12})^{59} \frac{1}{12}

Simplify

1000 \cdot 60 (1 + \frac{r}{12})^{59} \frac{1}{12} : 5000 (\frac{r}{12} + 1)^{59}

= 5000 (\frac{r}{12} + 1)^{59}

n = 1 \sum \infty \frac{1}{2}

1 - e^{- s}

\int (x^{3} (2 x^{2} - 3)) d x

\int (\frac{x}{3})^{3} d x

What is the derivative of 1000(1+r/(12))^{60} ?
The derivative of 1000(1+r/(12))^{60} is 5000(r/(12)+1)^{59}
What is the first derivative of 1000(1+r/(12))^{60} ?
The first derivative of 1000(1+r/(12))^{60} is 5000(r/(12)+1)^{59}