Find the derivative of the function y= x(7^-3x)

find the derivative of the function y= x(7^(-3x))

ALSO can someone help me on this problem?

use integration to find a general solution of the differential equation

# 42) dy/dx = 5 e^(-x/2)

thank you

1.
y = x(7^(-3x)) = x / 7^3x,

y' = 1/7^3x -(x)(3x)ln7/7^(3x+1)

y' = [7 - 3x^2ln7] / 7^(3x+1) >==============< ANSWER

2.
dy/dx = 5 e^(-x/2)

dy = 5 e^(-x/2).dx

y = 5(-1/2)e^(-x/2),

y = -2.5 e^(-x/2) + c >=================< ANSWER

That is a good question.
I tried to search the answer for you at several places and asked few friends.
I have some answers some are short, some partially right, and some are most irrelevant.
There is not an answer that will completely satisfy you.
My friend Diana mentioned about trying wish123 where she said you might find an answer at.
I don't post my questions on that very often though.
So I will leave it for you. Sorry couldn't help you more.
wish you good luck.
Kristy