# Please help! I don't know how to calculate?

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Let #f(x) = 2^x# . Using the chain rule, determine an expression for the derivative of #[f(g(x))]# .

Let

##### 1 Answer

Apr 26, 2018

If

#### Explanation:

Using the generic function

#f[g(x)] = 2^(g(x))#

Thus,

#d/dx f[g(x)] = d/dx 2^(g(x))#

The chain rule says: If

Basically, you treat

#d/dx f[g(x)] = (df)/(dg) * (dg)/dx#

#color(white)(d/dx f[g(x)]) = d/(dg) 2^g * d/dx g(x)#

#color(white)(d/dx f[g(x)]) = (ln 2)(2^g) * g'(x)#

#color(white)(d/dx f[g(x)]) = (ln 2)(2^(g(x)))g'(x)#