Question

find the derivative of the function


integral from cosx to sinx (ln(8+3v)dv)

Answer 1

the derivative of a definite integral is how much the area changes as you change the limits.

d/dx Int from p(x) to q(x) of f(v)dv
= [f(q)-f(p)]dx

(draw a sketch of that graph)

Answer 2

sorry, extra dx in there
= f(q) - f(p)

f(q) = ln (8+3sin x)
f(p) = ln (8+3cos x)

f(q)-f(p) = ln [ (8+3sin x)/(8+3cos x) ]

Answer 3

y'(x)= (sin(8+3((sin(x)))+x)+sin(8+3sin(x)-x))/2

Is this the right answer?????

Answer 4

Well, I gave you my answer which is quite different.