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Derivative of:
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
Derivative of 5*x^4-7*x^2-x
Derivative of 3x-x^2
Derivative of 4*sqrt(3)*x/3
Identical expressions
(5sin10x- three)/ one hundred
(5 sinus of 10x minus 3) divide by 100
(5 sinus of 10x minus three) divide by one hundred
5sin10x-3/100
(5sin10x-3) divide by 100
Similar expressions
(5sin10x+3)/100

The derivative of the function/ (5sin10x-3)/100

Derivative of (5sin10x-3)/100

The solution

You have entered [src]

5*sin(10*x) - 3
---------------
      100

$$\frac{5 \sin{\left(10 x \right)} - 3}{100}$$

(5*sin(10*x) - 3)/100

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $5 \sin{\left(10 x \right)} - 3$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = 10 x$ .
    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 $\frac{d}{d x} 10 x$ :
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $10$
      The result of the chain rule is:
      
      $10 \cos{\left(10 x \right)}$
    So, the result is: $50 \cos{\left(10 x \right)}$
  2. The derivative of the constant $-3$ is zero.
  The result is: $50 \cos{\left(10 x \right)}$
So, the result is: $\frac{\cos{\left(10 x \right)}}{2}$

The answer is:

$\frac{\cos{\left(10 x \right)}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(10*x)
---------
    2

$$\frac{\cos{\left(10 x \right)}}{2}$$

Simplify

The second derivative [src]

-5*sin(10*x)

$$- 5 \sin{\left(10 x \right)}$$

Simplify

The third derivative [src]

-50*cos(10*x)

$$- 50 \cos{\left(10 x \right)}$$

Simplify