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The derivative of the function/ z=siny+y^2-x2y

You entered:

z=siny+y^2-x2y

What you mean?

sin(y) + y^2 - x^2*y

Derivative of z=siny+y^2-x2y

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
          2       
sin(y) + y  - x2*y
−x2y+y2+sin⁡(y)- x_{2} y + y^{2} + \sin{\left(y \right)} 
d /          2       \
--\sin(y) + y  - x2*y/
dy
∂∂y(−x2y+y2+sin⁡(y))\frac{\partial}{\partial y} \left(- x_{2} y + y^{2} + \sin{\left(y \right)}\right)
Transform
Detail solution

  1. Differentiate −x2y+y2+sin⁡(y)- x_{2} y + y^{2} + \sin{\left(y \right)} term by term:

    1. The derivative of sine is cosine:

      ddysin⁡(y)=cos⁡(y)\frac{d}{d y} \sin{\left(y \right)} = \cos{\left(y \right)}

    2. Apply the power rule: y2y^{2} goes to 2y2 y

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

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

        1. Apply the power rule: yy goes to 11

        So, the result is: x2x_{2}

      So, the result is: −x2- x_{2}

    The result is: −x2+2y+cos⁡(y)- x_{2} + 2 y + \cos{\left(y \right)}

The answer is:

−x2+2y+cos⁡(y)- x_{2} + 2 y + \cos{\left(y \right)}

The first derivative [src] 
-x2 + 2*y + cos(y)
−x2+2y+cos⁡(y)- x_{2} + 2 y + \cos{\left(y \right)}
Simplify
The second derivative [src] 
2 - sin(y)
−sin⁡(y)+2- \sin{\left(y \right)} + 2
Simplify
The third derivative [src] 
-cos(y)
−cos⁡(y)- \cos{\left(y \right)}
Simplify
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