Question

Differentiate (2x^2+1) (3x+2)

Answer 1

Answer:

Express the terms of the function in exponent form.

⇒

1

3

x

−

2

−

5

2

x

−

1

differentiate each term using the

power rule

Reminder

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

d

d

x

(

a

x

n

)

=

n

a

x

n

−

1

2

2

∣

∣

∣

−−−−−−−−−−−−−−−−−−−−−−

⇒

d

d

x

(

1

3

x

−

2

−

5

2

x

−

1

)

=

−

2

3

x

−

3

+

5

2

x

−

2

=

5

2

x

2

−

2

3

x

3

Answer 2

Answer: 6x3+4x2+3x+2

Step-by-step explanation:

(2x2+1)(3x+2)

=(2x2+1)(3x+2)

=(2x2)(3x)+(2x2)(2)+(1)(3x)+(1)(2)

=6x3+4x2+3x+2