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y=sin(x^2-x+1)

Derivative of y=sin(x^2-x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   / 2        \
sin\x  - x + 1/
$$\sin{\left(x^{2} - x + 1 \right)}$$
d /   / 2        \\
--\sin\x  - x + 1//
dx                 
$$\frac{d}{d x} \sin{\left(x^{2} - x + 1 \right)}$$
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. Apply the power rule: goes to

      2. 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:

      3. 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        \
(-1 + 2*x)*cos\x  - x + 1/
$$\left(2 x - 1\right) \cos{\left(x^{2} - x + 1 \right)}$$
The second derivative [src]
     /     2    \             2    /     2    \
2*cos\1 + x  - x/ - (-1 + 2*x) *sin\1 + x  - x/
$$- \left(2 x - 1\right)^{2} \sin{\left(x^{2} - x + 1 \right)} + 2 \cos{\left(x^{2} - x + 1 \right)}$$
The third derivative [src]
            /     /     2    \             2    /     2    \\
-(-1 + 2*x)*\6*sin\1 + x  - x/ + (-1 + 2*x) *cos\1 + x  - x//
$$- \left(2 x - 1\right) \left(\left(2 x - 1\right)^{2} \cos{\left(x^{2} - x + 1 \right)} + 6 \sin{\left(x^{2} - x + 1 \right)}\right)$$
The graph
Derivative of y=sin(x^2-x+1)