Question

write differentiation of ( 2x square + 3)​

Answer 1

Explanation:

Apply the chain rule, which tells us that

d

d

x

(

f

(

g

(

x

)

)

=

f

'

(

g

(

x

)

)

⋅

g

'

(

x

)

.

For the function

(

2

x

−

3

)

5

,

we see it is a polynomial composed with an exponential function. So, the power rule is used to differentiate the polynomial raised to the

5

t

h

power, and the fact that

d

d

x

a

x

=

a

to differentiate the polynomial

2

x

−

3

d

d

x

(

2

x

−

3

)

5

=

5

(

2

x

−

3

)

5

−

1

⋅

d

d

x

(

2

x

−

3

)

=

(

2

)

(

5

)

(

2

x

−

3

)

4

=

10

(

2

x

−

3

)

4