# What is the derivative of the given function?

Which of these are correct form for $\large \frac{d}{dx} (4.7^{x+2.4})$? There may be more than one correct answer

    1. 4.7^(2.4) * 4.7^(x)ln*(4.7)
2. (x+2.4)(4.7^(x+1.4))
3. 2.4(4.7^(x+1.4))
4. (4.7^(x+2.4))ln(4.7)
5. 2.4(4.7^(x+1.4))ln(4.7)
6. All are correct
7. None are correct

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Welcome to MSE! It really helps readability to format thing using MathJax. I did part of it to show you, but it would help to format questions this way! Regards –  Amzoti Feb 1 '13 at 18:53

Since this is in the form of $y=a^{f(x)}$ to derive this its just $y'= (a^x)\cdot\ln x\cdot f'(x)$

so in your case we have $y=(4.7)^{(x+2.4)}$ and now if we apply that rule we will get

$$y' = [(4.7)^{(x+2.4)}]\cdot\ln(4.7)\cdot(1) = \left[(4.7)^{(x+2.4)}\right]\cdot\ln(4.7)$$

so the answer is $4$ but if you notice closely we can break up the exponent by the exponent laws

to obtain $\left(4.7^{2.4}\right)\cdot\left(4.7^x\right)\cdot(\ln 4.7)$ and this is answer 1 :)

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thank you! I had gotten 1 as an answer and wasnt really sure if any of the other ones were the same. :) –  user56852 Feb 1 '13 at 20:11
thanks brian for editing it, i wanted to know whats the language you guys use on here? latex? –  MathGeek Feb 2 '13 at 4:41

Hint: What is $4.7^{x + 2.4}$ written in terms of $\exp$ and $\ln$?