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The derivative of the function/ sin(12(x^2)+x)

Derivative of sin(12(x^2)+x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /    2    \
sin\12*x  + x/
$$\sin{\left(12 x^{2} + x \right)}$$ 
sin(12*x^2 + x)
Detail solution

  1. Let .

  2. The derivative of sine is cosine:

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

    1. Differentiate 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: goes to

        So, the result is:

      2. Apply the power rule: goes to

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              /    2    \
(1 + 24*x)*cos\12*x  + x/
$$\left(24 x + 1\right) \cos{\left(12 x^{2} + x \right)}$$
Simplify
The second derivative [src] 
                                 2                  
24*cos(x*(1 + 12*x)) - (1 + 24*x) *sin(x*(1 + 12*x))
$$- \left(24 x + 1\right)^{2} \sin{\left(x \left(12 x + 1\right) \right)} + 24 \cos{\left(x \left(12 x + 1\right) \right)}$$
Simplify
The third derivative [src] 
            /                                 2                  \
-(1 + 24*x)*\72*sin(x*(1 + 12*x)) + (1 + 24*x) *cos(x*(1 + 12*x))/
$$- \left(24 x + 1\right) \left(\left(24 x + 1\right)^{2} \cos{\left(x \left(12 x + 1\right) \right)} + 72 \sin{\left(x \left(12 x + 1\right) \right)}\right)$$
Simplify
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