Mister Exam

Derivative of sinx^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2   
sin (x)
sin2(x)\sin^{2}{\left(x \right)}
sin(x)^2
Detail solution
  1. Let u=sin(x)u = \sin{\left(x \right)}.

  2. Apply the power rule: u2u^{2} goes to 2u2 u

  3. Then, apply the chain rule. Multiply by ddxsin(x)\frac{d}{d x} \sin{\left(x \right)}:

    1. The derivative of sine is cosine:

      ddxsin(x)=cos(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

    The result of the chain rule is:

    2sin(x)cos(x)2 \sin{\left(x \right)} \cos{\left(x \right)}

  4. Now simplify:

    sin(2x)\sin{\left(2 x \right)}


The answer is:

sin(2x)\sin{\left(2 x \right)}

The graph
02468-8-6-4-2-10102-2
The first derivative [src]
2*cos(x)*sin(x)
2sin(x)cos(x)2 \sin{\left(x \right)} \cos{\left(x \right)}
The second derivative [src]
  /   2         2   \
2*\cos (x) - sin (x)/
2(sin2(x)+cos2(x))2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)
The third derivative [src]
-8*cos(x)*sin(x)
8sin(x)cos(x)- 8 \sin{\left(x \right)} \cos{\left(x \right)}
The graph
Derivative of sinx^2