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Derivative of:
Derivative of (x^2+49)/x
Derivative of sec2x
Derivative of x*e^x-e^x
Derivative of (x-3)/sqrt(x)
Identical expressions
zero .1sin(three -5x^ two)
0.1 sinus of (3 minus 5x squared )
zero .1 sinus of (three minus 5x to the power of two)
0.1sin(3-5x2)
0.1sin3-5x2
0.1sin(3-5x²)
0.1sin(3-5x to the power of 2)
0.1sin3-5x^2
Similar expressions
0.1sin(3+5x^2)

The derivative of the function/ 0.1sin(3-5x^2)

Derivative of 0.1sin(3-5x^2)

The solution

You have entered [src]

   /       2\
sin\3 - 5*x /
-------------
      10

$$\frac{\sin{\left(3 - 5 x^{2} \right)}}{10}$$

sin(3 - 5*x^2)/10

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 - 5 x^{2}$ .
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 $\frac{d}{d x} \left(3 - 5 x^{2}\right)$ :
  1. Differentiate $3 - 5 x^{2}$ term by term:
    1. The derivative of the constant $3$ is zero.
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      So, the result is: $- 10 x$
    The result is: $- 10 x$
  The result of the chain rule is:
  
  $- 10 x \cos{\left(5 x^{2} - 3 \right)}$
So, the result is: $- x \cos{\left(5 x^{2} - 3 \right)}$

The answer is:

$- x \cos{\left(5 x^{2} - 3 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      /        2\
-x*cos\-3 + 5*x /

$$- x \cos{\left(5 x^{2} - 3 \right)}$$

Simplify

The second derivative [src]

     /        2\       2    /        2\
- cos\-3 + 5*x / + 10*x *sin\-3 + 5*x /

$$10 x^{2} \sin{\left(5 x^{2} - 3 \right)} - \cos{\left(5 x^{2} - 3 \right)}$$

Simplify

The third derivative [src]

     /     /        2\       2    /        2\\
10*x*\3*sin\-3 + 5*x / + 10*x *cos\-3 + 5*x //

$$10 x \left(10 x^{2} \cos{\left(5 x^{2} - 3 \right)} + 3 \sin{\left(5 x^{2} - 3 \right)}\right)$$

Simplify