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3*x-cosx-1
The derivative of the function/ 3*x-cosx-1

Derivative of 3*x-cosx-1

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

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The solution

You have entered [src] 
3*x - cos(x) - 1
3x−cos⁡(x)−13 x - \cos{\left(x \right)} - 1 
d                   
--(3*x - cos(x) - 1)
dx
ddx(3x−cos⁡(x)−1)\frac{d}{d x} \left(3 x - \cos{\left(x \right)} - 1\right)
Transform
Detail solution

  1. Differentiate 3x−cos⁡(x)−13 x - \cos{\left(x \right)} - 1 term by term:

    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

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

      1. The derivative of cosine is negative sine:

        ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

      So, the result is: sin⁡(x)\sin{\left(x \right)}

    3. The derivative of the constant (−1)1\left(-1\right) 1 is zero.

    The result is: sin⁡(x)+3\sin{\left(x \right)} + 3

The answer is:

sin⁡(x)+3\sin{\left(x \right)} + 3

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
3 + sin(x)
sin⁡(x)+3\sin{\left(x \right)} + 3
Simplify
The second derivative [src] 
cos(x)
cos⁡(x)\cos{\left(x \right)}
Simplify
The third derivative [src] 
-sin(x)
−sin⁡(x)- \sin{\left(x \right)}
Simplify
The graph
Derivative of 3*x-cosx-1
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