Differentiating question

[cotfw]

This is the question:

e^ax / x^7/2


i tried the quotient rule, which left me with

(e^ax (x^7/2a - 7/2)) / x^7

but this is wrong apparently. I am finding it difficult to type using this iPad so I can't go into more detail

 

[pka]

This is the question:

e^ax / x^7/2
i tried the quotient rule, which left me with
(e^ax (x^7/2a - 7/2)) / x^7

\(\displaystyle {D_x}\left( {\dfrac{{{e^{ax}}}}{{{x^{7/2}}}}} \right) = \dfrac{{a{e^{ax}}{x^{7/2}} - {e^{ax}}\left[ {\left( {7/2} \right){x^{5/2}}} \right]}}{{{x^7}}}\)

 

[soroban]

Hello, cotfw!

Your Quotient Rule is incorrect.

\(\displaystyle y \:=\:\frac{e^{ax}}{x^{\frac{7}{2}}}\)

\(\displaystyle \dfrac{dy}{dx} \;=\; \dfrac{x^{\frac{7}{2}}\cdot ae^{ax} - e^{ax}\cdot\frac{7}{2}x^{\frac{5}{2}}}{x^7} \;=\;\dfrac{\frac{1}{2}x^{\frac {5}{2}}e^{ax}(2ax-7)}{x^7}
\;=\;\dfrac{e^{ax}(2ax-7)}{2x^{\frac{9}{2}}}\)

 

[HallsofIvy]

This is the question:

e^ax / x^7/2


i tried the quotient rule, which left me with

(e^ax (x^7/2a -

7/2​

)) / x^7

but this is wrong apparently. I am finding it difficult to type using this iPad so I can't go into more detail

That "a- 7/2" is your error. the derivative of \(\displaystyle x^{7/2}\) is \(\displaystyle (7/2)x^{5/2}\) not just "7/2"