Question

Differentiate with respect to x and simplify your answers wherever possible.
a. x^4 sin 2x
b. e^x In x
c. 3x / (1+sin x)
d. 2x+1 / x+3
e. x^3 In x
f. e^x sin2x
g. e^x / x
h. 2x/ x+3
I. log sin x

Answer 1

I already did ln cosx using the chain rule. ln sinx works the same way
The rest of these are just the product rule and the quotient rule.
(b) e^x lnx + e^x * 1/x = e^x (lnx + 1/x)
(c) ((3)(1+sinx) - (3x)(cosx))/(1+sinx)^2

see what you can do with the rest of these.