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Derivative of:
Derivative of tan(x/2)-cot(x/2)
Derivative of log(x+3)
Derivative of ln((x^2)/(1-x^2))
Derivative of cos(x)-log(x)
Identical expressions
- four /x^ four -5sinx
minus 4 divide by x to the power of 4 minus 5 sinus of x
minus four divide by x to the power of four minus 5 sinus of x
-4/x4-5sinx
-4/x⁴-5sinx
-4 divide by x^4-5sinx
Similar expressions
-4/x^4+5sinx
4/x^4-5sinx

The derivative of the function/ -4/x^4-5sinx

Derivative of -4/x^4-5sinx

The solution

You have entered [src]

  4            
- -- - 5*sin(x)
   4           
  x

$$- 5 \sin{\left(x \right)} - \frac{4}{x^{4}}$$

-4/x^4 - 5*sin(x)

Detail solution

Differentiate $- 5 \sin{\left(x \right)} - \frac{4}{x^{4}}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x^{4}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{4}$ :
    1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
    The result of the chain rule is:
    
    $- \frac{4}{x^{5}}$
  So, the result is: $\frac{16}{x^{5}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $- 5 \cos{\left(x \right)}$
The result is: $- 5 \cos{\left(x \right)} + \frac{16}{x^{5}}$

The answer is:

$- 5 \cos{\left(x \right)} + \frac{16}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            16
-5*cos(x) + --
             5
            x

$$- 5 \cos{\left(x \right)} + \frac{16}{x^{5}}$$

Simplify

The second derivative [src]

  /  16         \
5*|- -- + sin(x)|
  |   6         |
  \  x          /

$$5 \left(\sin{\left(x \right)} - \frac{16}{x^{6}}\right)$$

Simplify

The third derivative [src]

  /96         \
5*|-- + cos(x)|
  | 7         |
  \x          /

$$5 \left(\cos{\left(x \right)} + \frac{96}{x^{7}}\right)$$

Simplify