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Derivative of:
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Derivative of -3*x^3+2*x^2-x-5
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Identical expressions
y=sin^ three *x: three
y equally sinus of cubed multiply by x:3
y equally sinus of to the power of three multiply by x: three
y=sin3*x:3
y=sin³*x:3
y=sin to the power of 3*x:3
y=sin^3x:3
y=sin3x:3

The derivative of the function/ y=sin^3*x:3

Derivative of y=sin^3*x:3

The solution

You have entered [src]

   3   
sin (x)
-------
   3

$$\frac{\sin^{3}{\left(x \right)}}{3}$$

  /   3   \
d |sin (x)|
--|-------|
dx\   3   /

$$\frac{d}{d x} \frac{\sin^{3}{\left(x \right)}}{3}$$

Transform

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2          
sin (x)*cos(x)

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

Simplify

The second derivative [src]

 /   2           2   \       
-\sin (x) - 2*cos (x)/*sin(x)

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

Simplify

The third derivative [src]

 /       2           2   \       
-\- 2*cos (x) + 7*sin (x)/*cos(x)

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

Simplify

The graph

Derivative of y=sin^3*x:3