What is the derivative of 500(1+x/(1200)^{120}) ?

The derivative of 500(1+x/(1200)^{120}) is 50(x/(1200)+1)^{119}

What is the first derivative of 500(1+x/(1200)^{120}) ?

The first derivative of 500(1+x/(1200)^{120}) is 50(x/(1200)+1)^{119}

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\frac{d}{d x} (500 (1 + \frac{x}{1200})^{120})

50 (\frac{x}{1200} + 1)^{119}

Solution steps

\frac{d}{d x} (500 (1 + \frac{x}{1200})^{120})

Take the constant out:

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

= 500 \frac{d}{d x} ((1 + \frac{x}{1200})^{120})

Apply the chain rule:

120 (1 + \frac{x}{1200})^{119} \frac{d}{d x} (1 + \frac{x}{1200})

= 120 (1 + \frac{x}{1200})^{119} \frac{d}{d x} (1 + \frac{x}{1200})

\frac{d}{d x} (1 + \frac{x}{1200}) = \frac{1}{1200}

= 500 \cdot 120 (1 + \frac{x}{1200})^{119} \frac{1}{1200}

Simplify

500 \cdot 120 (1 + \frac{x}{1200})^{119} \frac{1}{1200} : 50 (\frac{x}{1200} + 1)^{119}

= 50 (\frac{x}{1200} + 1)^{119}

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What is the derivative of 500(1+x/(1200)^{120}) ?
The derivative of 500(1+x/(1200)^{120}) is 50(x/(1200)+1)^{119}
What is the first derivative of 500(1+x/(1200)^{120}) ?
The first derivative of 500(1+x/(1200)^{120}) is 50(x/(1200)+1)^{119}