Question

If
y = 2e" sinx
then
dy
dan
is​

Answer 1

Step-by-step explanation:

Steps:

ddx(x2exsin(x))

Apply the power rule: (f⋅g)′=f′⋅g+f⋅g′f=x2,g=exsin(x)

=ddx(x2)exsin(x)+ddx(exsin(x))x2

Solving for ddx(x2):

Apply the power rule: ddx(xa)=a⋅xa−1

=2x2−1→=2x

Solving for ddx(exsin(x))

Apply the power rule: (f⋅g)′=f′⋅g+f⋅g′f=x2,g=exsin(x)

=ddx(ex)sin(x)+ddx(sin(x))ex

Solving for ddx(ex)

Apply the common derivative: ddx(ex)=ex

=ex

Solving for ddx(sin(x))

Apply the common derivative: ddx(sin(x))=cos(x)

=cos(x)

Plugging in all solved derivatives:

ddx(x2)exsin(x)+ddx(exsin(x))x2=2xexsin(x)+exx2sin(x)+cos(x)x2ex

Rearrange and simplify:

=x2exsin(x)+2xexsin(x)+x2excos(x)=xex((x+2)sin(x)+xcos(x))