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sin(2*x^2+3)

Derivative of sin(2*x^2+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   2    \
sin\2*x  + 3/
$$\sin{\left(2 x^{2} + 3 \right)}$$
sin(2*x^2 + 3)
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. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
       /   2    \
4*x*cos\2*x  + 3/
$$4 x \cos{\left(2 x^{2} + 3 \right)}$$
The second derivative [src]
  /     2    /       2\      /       2\\
4*\- 4*x *sin\3 + 2*x / + cos\3 + 2*x //
$$4 \left(- 4 x^{2} \sin{\left(2 x^{2} + 3 \right)} + \cos{\left(2 x^{2} + 3 \right)}\right)$$
The third derivative [src]
      /     /       2\      2    /       2\\
-16*x*\3*sin\3 + 2*x / + 4*x *cos\3 + 2*x //
$$- 16 x \left(4 x^{2} \cos{\left(2 x^{2} + 3 \right)} + 3 \sin{\left(2 x^{2} + 3 \right)}\right)$$
The graph
Derivative of sin(2*x^2+3)