How do you differentiate y=tlog3e^sinty=tlog3esint?

1 Answer
Apr 26, 2017

Please see the explanation.

Explanation:

Given: y=tlog(3e^sin(t))y=tlog(3esin(t))

Using the property log(a^c) = (c)log(x)log(ac)=(c)log(x)

y = tsin(t)log(3e)y=tsin(t)log(3e)

Differentiate:

dy/dt = d/dttsin(t)log(3e)dydt=ddttsin(t)log(3e)

Use the property that the derivative is a linear operation:

dy/dt = log(3e)d/dttsin(t)dydt=log(3e)ddttsin(t)

Apply the product rule:

dy/dt = log(3e)(dt/dtsin(t) + td/dtsin(t))dydt=log(3e)(dtdtsin(t)+tddtsin(t))

Simplify:

dy/dt = log(3e)(sin(t) + tcos(t))dydt=log(3e)(sin(t)+tcos(t))