Mister Exam

Other calculators

The derivative of the function/ (sin^7x)/7

Derivative of (sin^7x)/7

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   7   
sin (x)
-------
   7
$$\frac{\sin^{7}{\left(x \right)}}{7}$$ 
  /   7   \
d |sin (x)|
--|-------|
dx\   7   /
$$\frac{d}{d x} \frac{\sin^{7}{\left(x \right)}}{7}$$
Transform
Detail solution

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

    1. Let .

    2. Apply the power rule: goes to

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

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    So, the result is:

The answer is:

The first derivative [src] 
   6          
sin (x)*cos(x)
$$\sin^{6}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
    5    /   2           2   \
-sin (x)*\sin (x) - 6*cos (x)/
$$- \left(\sin^{2}{\left(x \right)} - 6 \cos^{2}{\left(x \right)}\right) \sin^{5}{\left(x \right)}$$
Simplify
The third derivative [src] 
    4    /        2            2   \       
-sin (x)*\- 30*cos (x) + 19*sin (x)/*cos(x)
$$- \left(19 \sin^{2}{\left(x \right)} - 30 \cos^{2}{\left(x \right)}\right) \sin^{4}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
    © Mister Exam – Calculator