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y=e^-cos5x
The derivative of the function/ y=e^-cos5x

You entered:

y=e^-cos5x

What you mean?

5*x/e^(1*cos(x))

Derivative of y=e^-cos5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -cos(5*x)
e
$$e^{- \cos{\left(5 x \right)}}$$ 
d / -cos(5*x)\
--\e         /
dx
$$\frac{d}{d x} e^{- \cos{\left(5 x \right)}}$$
Transform
Detail solution

  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

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

      1. Let .

      2. The derivative of cosine is negative sine:

      3. Then, apply the chain rule. Multiply by :

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

          1. Apply the power rule: goes to

          So, the result is:

        The result of the chain rule is:

      So, the result is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   -cos(5*x)         
5*e         *sin(5*x)
$$5 e^{- \cos{\left(5 x \right)}} \sin{\left(5 x \right)}$$
Simplify
The second derivative [src] 
   /   2                \  -cos(5*x)
25*\sin (5*x) + cos(5*x)/*e
$$25 \left(\sin^{2}{\left(5 x \right)} + \cos{\left(5 x \right)}\right) e^{- \cos{\left(5 x \right)}}$$
Simplify
The third derivative [src] 
    /        2                  \  -cos(5*x)         
125*\-1 + sin (5*x) + 3*cos(5*x)/*e         *sin(5*x)
$$125 \left(\sin^{2}{\left(5 x \right)} + 3 \cos{\left(5 x \right)} - 1\right) e^{- \cos{\left(5 x \right)}} \sin{\left(5 x \right)}$$
Simplify
The graph
Derivative of y=e^-cos5x
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