Differentiate the following with respect to x: e^(10x) + ln(6x+2)

We can differentiate the terms separately:
The first term e^10x can be differentiated using the chain rule.
Let u = 10xWe can differentiate to get du/dx = 10
Differentiating e^u with respect to u gives us d/du = e^u
the differential of e^10x is d/du x du/dx = 10e^u
the two du's cancel out and we can replace u with 10x to get:
d/dx = 10e^10x
The second term Ln(6x+2) can also be differentiated using the chain rule.
Let v = 6x+2We can differentiate to get dv/dx = 6
Differentiating ln(v) with respect to v gives us 1/v. The differential of ln(6x+2) is (dv/dx) x (d/dv) = 6/v
which gives us d/dx = 6/(6x+2)
The final answer
10e^10x + 6/(6x+2)
You can simplify the second fraction by diving by 2 from the top and bottom:
10e^10x + 3/(3x+1)