calculus - derivatives

Question

Differentiate the following functions. A, B, and C are constants.

(a) g(x) = Ae^x cos(Bx)

(b) h(x) = ln(Cx^5 )

Answer 1

Hello again Roz A.,

(a) requires applying the rule for differential of product of functions:

d(f(x)*g(x))/dx = f(x)*d(g(x))/dx + g(x)*d(f(x))/d(x) and also you need to know the specific differentials for e^x and cos(x) -- note that you require the chain rule for cos(nx) !

(b) requires the specific differential for ln(x), and also the chain rule twice because of the Cx^5 argument.

Example of Chain Rule: d(Cx^5)/dx = C*d(x^5)/dx =5*C*d(x)/d(x)= 5*C . So what the Chain Rule states, in simplest form, is that the differentiation proceeds to drill down towards just x in stages, one stage per arithmetic operation inside which x is embedded. So in the above example, x was embedded twice: once as x^5 power, and once as *C. To "unembed" the x, that process proceeds from the "outside" in, just like you would solve an equation, for example.

Hope that gets you where you need to be to start solving these on your own, that's what you need to do.

-- Cheers, --Mr. d.

Answer 2

You asked this same question yesterday and I already posted an answer to it.