Question

Some one please EXPLAIN this to me

Answer 1

\[\huge y= 2(3^x)\]
\[\huge y'= 2 (3^x)(\ln3)\]

Answer 2

For the derivative ... Why does the 2 remain ? Shouldn't this be a product rule question ?

Answer 3

2 is a constant
constants are unaffected when finding the derivative

Answer 4

well not unaffected, you could product rule but the derivative of a constant is 0 and thus it would cancel out

Answer 5

\[\large y=c*a^x\]\[\large \frac{d}{dx}(c*a^x) = c*a^x *\frac{d}{dx}(x) * \ln a\]

Answer 6

product rules involves 2 functions

Answer 7

Say your problem was \[\huge y= 2(3^{\frac{1}{2}x})\] your derivative would be \[\large \frac{dy}{dx}= 2*(3^{\frac{1}{2}x}) * \frac{1}{2} *\ln (3) = 3^{\frac{1}{2}x} * \ln(3)\]

Answer 8

OHHH !

Answer 9

I was just elaborating...

Answer 10

@Jhannybean i like the way you explained it !

Answer 11

Thanks, I was eaborating @completeidiot 's point in my POV...

Answer 12

Here's another view using implicit differentiation:
\[y=2(3^{x})\]
\[\ln y = \ln 2 + x \ln 3\]
Differentiate:
\[\frac{ 1 }{ y }y'=\ln 3\]
\[y'=2(3^{x})\ln 3\]

Answer 13

Yess! implicit differentiation :)