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cos(5*x)
The derivative of the function/ cos(5*x)

Derivative of cos(5*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
cos(5*x)
cos⁡(5x)\cos{\left(5 x \right)} 
cos(5*x)
Detail solution

  1. Let u=5xu = 5 x.

  2. The derivative of cosine is negative sine:

    dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ddx5x\frac{d}{d x} 5 x:

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

      1. Apply the power rule: xx goes to 11

      So, the result is: 55

    The result of the chain rule is:

    −5sin⁡(5x)- 5 \sin{\left(5 x \right)}

The answer is:

−5sin⁡(5x)- 5 \sin{\left(5 x \right)}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-5*sin(5*x)
−5sin⁡(5x)- 5 \sin{\left(5 x \right)}
Simplify
The second derivative [src] 
-25*cos(5*x)
−25cos⁡(5x)- 25 \cos{\left(5 x \right)}
Simplify
The third derivative [src] 
125*sin(5*x)
125sin⁡(5x)125 \sin{\left(5 x \right)}
Simplify
The graph
Derivative of cos(5*x)
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