Mister Exam

Other calculators


y=sin(x)*cos^3(x)

Derivative of y=sin(x)*cos^3(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
          3   
sin(x)*cos (x)
$$\sin{\left(x \right)} \cos^{3}{\left(x \right)}$$
sin(x)*cos(x)^3
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of sine is cosine:

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

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

      1. The derivative of cosine is negative sine:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   4           2       2   
cos (x) - 3*cos (x)*sin (x)
$$- 3 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{4}{\left(x \right)}$$
The second derivative [src]
/        2           2   \              
\- 10*cos (x) + 6*sin (x)/*cos(x)*sin(x)
$$\left(6 \sin^{2}{\left(x \right)} - 10 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
The third derivative [src]
     4           2    /       2           2   \        2       2           2    /     2           2   \
- cos (x) - 3*sin (x)*\- 7*cos (x) + 2*sin (x)/ + 9*cos (x)*sin (x) + 9*cos (x)*\- cos (x) + 2*sin (x)/
$$- 3 \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} + 9 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} + 9 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} - \cos^{4}{\left(x \right)}$$
The graph
Derivative of y=sin(x)*cos^3(x)