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Popular >

derivative of 1000(1+x/(12)^{60})

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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