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y=(sinx/1+cosx)^2
The derivative of the function/ y=(sinx/1+cosx)^2

Derivative of y=(sinx/1+cosx)^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                 2
/sin(x)         \ 
|------ + cos(x)| 
\  1            /
$$\left(\frac{\sin{\left(x \right)}}{1} + \cos{\left(x \right)}\right)^{2}$$ 
  /                 2\
d |/sin(x)         \ |
--||------ + cos(x)| |
dx\\  1            / /
$$\frac{d}{d x} \left(\frac{\sin{\left(x \right)}}{1} + \cos{\left(x \right)}\right)^{2}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  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. The derivative of sine is cosine:

        So, the result is:

      2. The derivative of cosine is negative sine:

      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] 
                       /sin(x)         \
(-2*sin(x) + 2*cos(x))*|------ + cos(x)|
                       \  1            /
$$\left(\frac{\sin{\left(x \right)}}{1} + \cos{\left(x \right)}\right) \left(- 2 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)$$
Simplify
The second derivative [src] 
  /                  2                    2\
2*\(-cos(x) + sin(x))  - (cos(x) + sin(x)) /
$$2 \left(\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} - \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}\right)$$
Simplify
The third derivative [src] 
8*(-cos(x) + sin(x))*(cos(x) + sin(x))
$$8 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
Simplify
The graph
Derivative of y=(sinx/1+cosx)^2
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