Question

what is the nth derivative of (e^3x) * (sin^2 4x)​

Answer 1

Answer:

Its simple, just need application of Product and Chain Rule for Diffrentiation.

for reminder:

Product Rule :

[f(x)g(x)]′=f′(x)g(x)+f(x)g′(x)

Chain Rule :

[f(g(x))]′=f′(g(x)) . g′(x)

Now for further answer, I will use Leibnitz Notation

ddx(e3xsin4x)=sin4xddx(e3x)+e3xddx(sin4x)

Now,

ddx(e3x)=de3xd(3x).d(3x)dx

=3e3x

For sine function:

ddx(sin4x)=d(sin4x)d(4x).d(4x)dx

=4cos4x

Putting these results in above expression:

ddx(e3xsin4x)

=3e3xsin4x+4e3xcos4x

Which is the required solution.

Hope it helps!

Answer 2

Step-by-step explanation:

refer the attachment in the top