Question

if y = sin^5(3x+1) then dy/dx =

Answer 1

Step-by-step explanation:

Given:

y

=

sin

(

3

x

)

.

Use the chain rule, which states that,

d

y

d

x

=

d

y

d

u

⋅

d

u

d

x

Let

u

=

3

x

,

∴

d

u

d

x

=

3

.

Then,

y

=

sin

(

u

)

,

∴

d

y

d

u

=

cos

(

u

)

.

Combining our results, we get,

d

y

d

x

=

cos

(

u

)

⋅

3

=

3

cos

(

u

)

Substitute back

u

=

3

x

, we get:

=

3

cos

(

3

x

)