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-1/3*sin(3x)
The derivative of the function/ -1/3*sin(3x)

Derivative of -1/3*sin(3x)

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

The graph:

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The solution

You have entered [src] 
-sin(3*x) 
----------
    3
−sin⁡(3x)3- \frac{\sin{\left(3 x \right)}}{3} 
d /-sin(3*x) \
--|----------|
dx\    3     /
ddx(−sin⁡(3x)3)\frac{d}{d x} \left(- \frac{\sin{\left(3 x \right)}}{3}\right)
Transform
Detail solution

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

    1. Let u=3xu = 3 x.

    2. The derivative of sine is cosine:

      ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}

    3. Then, apply the chain rule. Multiply by ddx3x\frac{d}{d x} 3 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: 33

      The result of the chain rule is:

      3cos⁡(3x)3 \cos{\left(3 x \right)}

    So, the result is: −cos⁡(3x)- \cos{\left(3 x \right)}

The answer is:

−cos⁡(3x)- \cos{\left(3 x \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-cos(3*x)
−cos⁡(3x)- \cos{\left(3 x \right)}
Simplify
The second derivative [src] 
3*sin(3*x)
3sin⁡(3x)3 \sin{\left(3 x \right)}
Simplify
The third derivative [src] 
9*cos(3*x)
9cos⁡(3x)9 \cos{\left(3 x \right)}
Simplify
The graph
Derivative of -1/3*sin(3x)
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