Mister Exam

Derivative of cos(3x+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(3*x + 2)
cos(3x+2)\cos{\left(3 x + 2 \right)}
cos(3*x + 2)
Detail solution
  1. Let u=3x+2u = 3 x + 2.

  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 ddx(3x+2)\frac{d}{d x} \left(3 x + 2\right):

    1. Differentiate 3x+23 x + 2 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 the constant 22 is zero.

      The result is: 33

    The result of the chain rule is:

    3sin(3x+2)- 3 \sin{\left(3 x + 2 \right)}

  4. Now simplify:

    3sin(3x+2)- 3 \sin{\left(3 x + 2 \right)}


The answer is:

3sin(3x+2)- 3 \sin{\left(3 x + 2 \right)}

The graph
02468-8-6-4-2-10105-5
The first derivative [src]
-3*sin(3*x + 2)
3sin(3x+2)- 3 \sin{\left(3 x + 2 \right)}
The second derivative [src]
-9*cos(2 + 3*x)
9cos(3x+2)- 9 \cos{\left(3 x + 2 \right)}
The third derivative [src]
27*sin(2 + 3*x)
27sin(3x+2)27 \sin{\left(3 x + 2 \right)}
The graph
Derivative of cos(3x+2)