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Derivative of:
Derivative of log((x+1)/(x-1))
Derivative of 8*sin(t)^(3)
Derivative of (1-sin(2*x))/(1+cos(2*x))
Derivative of 16tgx
Identical expressions
eight *sin(t)^(three)
8 multiply by sinus of (t) to the power of (3)
eight multiply by sinus of (t) to the power of (three)
8*sin(t)(3)
8*sint3
8sin(t)^(3)
8sin(t)(3)
8sint3
8sint^3

The derivative of the function/ 8*sin(t)^(3)

Derivative of 8*sin(t)^(3)

The solution

You have entered [src]

     3   
8*sin (t)

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

8*sin(t)^3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sin{\left(t \right)}$ .
2. Apply the power rule: $u^{3}$ goes to $3 u^{2}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d t} \sin{\left(t \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d t} \sin{\left(t \right)} = \cos{\left(t \right)}$
  The result of the chain rule is:
  
  $3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}$
So, the result is: $24 \sin^{2}{\left(t \right)} \cos{\left(t \right)}$

The answer is:

$24 \sin^{2}{\left(t \right)} \cos{\left(t \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2          
24*sin (t)*cos(t)

$$24 \sin^{2}{\left(t \right)} \cos{\left(t \right)}$$

Simplify

The second derivative [src]

    /   2           2   \       
-24*\sin (t) - 2*cos (t)/*sin(t)

$$- 24 \left(\sin^{2}{\left(t \right)} - 2 \cos^{2}{\left(t \right)}\right) \sin{\left(t \right)}$$

Simplify

The third derivative [src]

    /       2           2   \       
-24*\- 2*cos (t) + 7*sin (t)/*cos(t)

$$- 24 \left(7 \sin^{2}{\left(t \right)} - 2 \cos^{2}{\left(t \right)}\right) \cos{\left(t \right)}$$

Simplify

The graph

Derivative of 8*sin(t)^(3)