Mister Exam

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The derivative of the function/ sinxsinx

Derivative of sinxsinx

The solution

You have entered [src]

sin(x)*sin(x)

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

sin(x)*sin(x)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
$g{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
The result is: $2 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*cos(x)*sin(x)

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

Simplify

The second derivative [src]

  /   2         2   \
2*\cos (x) - sin (x)/

$$2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

-8*cos(x)*sin(x)

$$- 8 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify