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  • Derivative of:
  • Derivative of 2/e^x Derivative of 2/e^x
  • Derivative of x^3*lnx Derivative of x^3*lnx
  • Derivative of 2/(x+1) Derivative of 2/(x+1)
  • Derivative of y=2x-1 Derivative of y=2x-1

  • Identical expressions

  • e^(sin^ two)*2sinx*cosx
  • e to the power of ( sinus of squared ) multiply by 2 sinus of x multiply by co sinus of e of x
  • e to the power of ( sinus of to the power of two) multiply by 2 sinus of x multiply by co sinus of e of x
  • e(sin2)*2sinx*cosx
  • esin2*2sinx*cosx
  • e^(sin²)*2sinx*cosx
  • e to the power of (sin to the power of 2)*2sinx*cosx
  • e^(sin^2)2sinxcosx
  • e(sin2)2sinxcosx
  • esin22sinxcosx
  • e^sin^22sinxcosx
The derivative of the function/ e^(sin^2)*2sinx*cosx

Derivative of e^(sin^2)*2sinx*cosx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    2                   
 sin (E)                
E       *2*sin(x)*cos(x)
$$2 e^{\sin^{2}{\left(e \right)}} \sin{\left(x \right)} \cos{\left(x \right)}$$ 
((E^(sin(E)^2)*2)*sin(x))*cos(x)
Detail solution

  1. Apply the product rule:

    ; to find :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

      So, the result is:

    ; to find :

    1. The derivative of cosine is negative sine:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                2                    2   
       2     sin (E)        2     sin (E)
- 2*sin (x)*e        + 2*cos (x)*e
$$- 2 e^{\sin^{2}{\left(e \right)}} \sin^{2}{\left(x \right)} + 2 e^{\sin^{2}{\left(e \right)}} \cos^{2}{\left(x \right)}$$
Simplify
The second derivative [src] 
              2          
           sin (E)       
-8*cos(x)*e       *sin(x)
$$- 8 e^{\sin^{2}{\left(e \right)}} \sin{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The third derivative [src] 
                          2   
  /   2         2   \  sin (E)
8*\sin (x) - cos (x)/*e
$$8 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) e^{\sin^{2}{\left(e \right)}}$$
Simplify
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