Mister Exam

Derivative of y=sin5x²

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2     
sin (5*x)
$$\sin^{2}{\left(5 x \right)}$$
d /   2     \
--\sin (5*x)/
dx           
$$\frac{d}{d x} \sin^{2}{\left(5 x \right)}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. The derivative of sine is cosine:

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

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

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
10*cos(5*x)*sin(5*x)
$$10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}$$
The second derivative [src]
   /   2           2     \
50*\cos (5*x) - sin (5*x)/
$$50 \left(- \sin^{2}{\left(5 x \right)} + \cos^{2}{\left(5 x \right)}\right)$$
The third derivative [src]
-1000*cos(5*x)*sin(5*x)
$$- 1000 \sin{\left(5 x \right)} \cos{\left(5 x \right)}$$
The graph
Derivative of y=sin5x²