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sin^(two)(x^ two - three)
sinus of to the power of (2)(x squared minus 3)
sinus of to the power of (two)(x to the power of two minus three)
sin(2)(x2-3)
sin2x2-3
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sin^2x^2-3
Similar expressions
sin^(2)(x^2+3)

The derivative of the function/ sin^(2)(x^2-3)

Derivative of sin^(2)(x^2-3)

The solution

You have entered [src]

   2/ 2    \
sin \x  - 3/

$$\sin^{2}{\left(x^{2} - 3 \right)}$$

d /   2/ 2    \\
--\sin \x  - 3//
dx

$$\frac{d}{d x} \sin^{2}{\left(x^{2} - 3 \right)}$$

Transform

Detail solution

Let $u = \sin{\left(x^{2} - 3 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x^{2} - 3 \right)}$ :
1. Let $u = x^{2} - 3$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 3\right)$ :
  1. Differentiate $x^{2} - 3$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of the constant $\left(-1\right) 3$ is zero.
    The result is: $2 x$
  The result of the chain rule is:
  
  $2 x \cos{\left(x^{2} - 3 \right)}$
The result of the chain rule is:

$4 x \sin{\left(x^{2} - 3 \right)} \cos{\left(x^{2} - 3 \right)}$
Now simplify:

$2 x \sin{\left(2 x^{2} - 6 \right)}$

The answer is:

$2 x \sin{\left(2 x^{2} - 6 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       / 2    \    / 2    \
4*x*cos\x  - 3/*sin\x  - 3/

$$4 x \sin{\left(x^{2} - 3 \right)} \cos{\left(x^{2} - 3 \right)}$$

Simplify

The second derivative [src]

  /   /      2\    /      2\      2    2/      2\      2    2/      2\\
4*\cos\-3 + x /*sin\-3 + x / - 2*x *sin \-3 + x / + 2*x *cos \-3 + x //

$$4 \left(- 2 x^{2} \sin^{2}{\left(x^{2} - 3 \right)} + 2 x^{2} \cos^{2}{\left(x^{2} - 3 \right)} + \sin{\left(x^{2} - 3 \right)} \cos{\left(x^{2} - 3 \right)}\right)$$

Simplify

The third derivative [src]

    /       2/      2\        2/      2\      2    /      2\    /      2\\
8*x*\- 3*sin \-3 + x / + 3*cos \-3 + x / - 8*x *cos\-3 + x /*sin\-3 + x //

$$8 x \left(- 8 x^{2} \sin{\left(x^{2} - 3 \right)} \cos{\left(x^{2} - 3 \right)} - 3 \sin^{2}{\left(x^{2} - 3 \right)} + 3 \cos^{2}{\left(x^{2} - 3 \right)}\right)$$

Simplify

The graph

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Derivative of sin^(2)(x^2-3)

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