Derivatives of Exponential Function y= (7^x)(e^2x)

[kimmy_koo51]

Find the derivatice of y= (7^x)(e^2x)

My work so far..

y= (7^x)(e^2x)
ln y = x ln 7 + 2x
1/y dy/dx = ln 7 + x + 2

dy/dx = (ln 7 + x + 2) [(7^x)(e^2x)]

Is this correct?

 

[pka]

\(\displaystyle \L b > 0\quad ,\quad y = b^x \quad \Rightarrow \quad y' = \left( {b^x } \right)\ln (b)\)

 

[kimmy_koo51]

Okay....

So then:

y= (7^x)(e^2x)
y'= (7^x ln)(e^2x) + (7^x)(2e^2x)
I'm not sure if you can simplify this like this but I will do it and inquire
y'= (7^x ln)(e^2x) + (14e^3x)

Can I do that?

 

[pka]

y= (7^x)(e^2x)
y'= (7^x ln)(e^2x) + (7^x)(2e^2x)

No
\(\displaystyle y = 7^x e^{2x} \quad \Rightarrow \quad y' = 7^x e^{2x} \ln (7) + 2\left( {7^x e^{2x} } \right).\)

 

[kimmy_koo51]

Oh right...opps thanks a lot.