How do you differentiate x⋅sin(2x)?
Answers
Answered by
1
Let the function be defined as
y = x*sin(2x)
Here, we have to apply the product rule for differentiation, that is partially differentiating each of the componental functions individually.
So,
dy/dx = x*d(sin2x)/dx + sin2x * d(x)/dx
= x * d(sin2x)/d (2x) * d(2x)/dx + sin 2x * d(x)/dx
= 2 x cos 2x + sin 2x (1)
Therefore,
dy/dx = 2x cos 2x + sin 2x
Answered by
0
Answer:
acobi J.
Jun 20, 2018
2
cos
2
x
Explanation:
The key realization is that we have a composite function, which can be differentiated with the help of the Chain Rule
f
'
(
g
(
x
)
)
⋅
g
'
(
x
)
We essentially have a composite function
f
(
g
(
x
)
)
where
f
(
x
)
=
sin
x
⇒
f
'
(
x
)
=
cos
x
and
g
(
x
)
=
2
x
⇒
g
'
(
x
)
=
2
We know all of the values we need to plug in, so let's do that. We get
cos
(
2
x
)
⋅
2
⇒
2
cos
2
x
Hope this helps!
Similar questions