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Derivative of:
Derivative of x+2
Derivative of (t^2-3)^4
Derivative of ctgx
Derivative of cos^2x^2
Identical expressions
(t^ two - three)^ four
(t squared minus 3) to the power of 4
(t to the power of two minus three) to the power of four
(t2-3)4
t2-34
(t²-3)⁴
(t to the power of 2-3) to the power of 4
t^2-3^4
Similar expressions
(t^2+3)^4

The derivative of the function/ (t^2-3)^4

Derivative of (t^2-3)^4

The solution

You have entered [src]

        4
/ 2    \ 
\t  - 3/

$$\left(t^{2} - 3\right)^{4}$$

  /        4\
d |/ 2    \ |
--\\t  - 3/ /
dt

$$\frac{d}{d t} \left(t^{2} - 3\right)^{4}$$

Transform

Detail solution

Let $u = t^{2} - 3$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
Then, apply the chain rule. Multiply by $\frac{d}{d t} \left(t^{2} - 3\right)$ :
1. Differentiate $t^{2} - 3$ term by term:
  1. Apply the power rule: $t^{2}$ goes to $2 t$
  2. The derivative of the constant $\left(-1\right) 3$ is zero.
  The result is: $2 t$
The result of the chain rule is:

$8 t \left(t^{2} - 3\right)^{3}$
Now simplify:

$8 t \left(t^{2} - 3\right)^{3}$

The answer is:

$8 t \left(t^{2} - 3\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            3
    / 2    \ 
8*t*\t  - 3/

$$8 t \left(t^{2} - 3\right)^{3}$$

Simplify

The second derivative [src]

           2            
  /      2\  /        2\
8*\-3 + t / *\-3 + 7*t /

$$8 \left(t^{2} - 3\right)^{2} \cdot \left(7 t^{2} - 3\right)$$

Simplify

The third derivative [src]

     /        2\ /      2\
48*t*\-9 + 7*t /*\-3 + t /

$$48 t \left(t^{2} - 3\right) \left(7 t^{2} - 9\right)$$

Simplify

The graph

Derivative of (t^2-3)^4