What is the derivative of the given function?

Question

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

Answer 1

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 :)

Answer 2

(8) Do your own homework

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

Answer 3

The answers 1 and 4 are actually the same and they are both correct.