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y=e^-1/2sin(2x)

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Derivative of:
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Derivative of y=ax^2+bx+c
Derivative of (sin3x)^x
Derivative of ln*sinx
Identical expressions
y=e^- one /2sin(2x)
y equally e to the power of minus 1 divide by 2 sinus of (2x)
y equally e to the power of minus one divide by 2 sinus of (2x)
y=e-1/2sin(2x)
y=e-1/2sin2x
y=e^-1/2sin2x
y=e^-1 divide by 2sin(2x)
Similar expressions
y=e^+1/2sin(2x)

The derivative of the function/ y=e^-1/2sin(2x)

Derivative of y=e^-1/2sin(2x)

The solution

You have entered [src]

sin(2*x)
--------
   ___  
 \/ E

$$\frac{\sin{\left(2 x \right)}}{e^{\frac{1}{2}}}$$

sin(2*x)/sqrt(E)

Detail solution

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

The answer is:

$\frac{2 \cos{\left(2 x \right)}}{e^{\frac{1}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            -1/2
2*cos(2*x)*e

$$\frac{2 \cos{\left(2 x \right)}}{e^{\frac{1}{2}}}$$

Simplify

The second derivative [src]

    -1/2         
-4*e    *sin(2*x)

$$- \frac{4 \sin{\left(2 x \right)}}{e^{\frac{1}{2}}}$$

Simplify

The third derivative [src]

             -1/2
-8*cos(2*x)*e

$$- \frac{8 \cos{\left(2 x \right)}}{e^{\frac{1}{2}}}$$

Simplify

The graph

Derivative of y=e^-1/2sin(2x)