differentiate (2x^2+3)^4?

Question

Answer according to pure mathematics explaining every step

Answer 1

y = (2x^2+3)^4
Let u = 2x^2 + 3
du/dx = 4x

y = u^4
dy/du = 4u^3
= 4(2x^2+3)^3

dy/dx = dy/dx * du/dx
= 4(2x^2+3)^3 * 4x
= 16x * (2x^2+3)^3

Answer 2

1. differentiate the power so it become like this
4 (2x^2+3) ^ (4 -1)
= 4 (2x^2+3) ^ 3

2. differentiate inside
4 (2x^2+3) ^ 3 (4x)
= 16x (2x^2 + 3)^3 final answer

Answer 3

Briing the power 4 down, multipy by the deriviative of the inside (d/dx (2x^2 + 3) = 4x) and multiply by the same function, but bring the power of 4 down to 3:
d/dx = 4(4x) (2x^2 + 3)^3
= 16x (2x^2 +3)^3

Answer 4

1. expand the expression
(2^4*x^[2*4])+3^4

2. the answer is: 16x^4+81

3. since 81 is a constant, it is eliminated from the expression
before differentiating:
16x^4

4. now for differentiation:
follow the rule: (p-1)(constant)x^(p-1)
; p is the power
(4-1)(16)x^(4-1)
3(16)x^3
48x^3

hope u get it!
5.

Answer 5

f (x) = (2 x ² + 3) ^(4)
f ` (x) = 4 (2 x ² + 3) ³ (4 x + 3)
Explanation
In layman`s terms the steps are:-
(i) differentiate the brackets
(ii) differentiate what is inside brackets
(iii) multiply the two expressions.

Answer 6

d (2X^2 + 3) 4
= d(8X^2 + 12)
= 16X + c

d* - means differential.

Answer 7

= 4(2x^2 + 3)^3 * (4x)

= 16x(2x^2 + 3)^3

Answer 8

You can not differentiate a constant. The result is zero.

Answer 9

Do you're own homework.

If you can't do it then fail whatever class it was set for.