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Derivative of x^2
Derivative of sec²x
Derivative of 10x^2
Derivative of cos^25x-sin^25x
Identical expressions
y= eight /x^ four -4sinx
y equally 8 divide by x to the power of 4 minus 4 sinus of x
y equally eight divide by x to the power of four minus 4 sinus of x
y=8/x4-4sinx
y=8/x⁴-4sinx
y=8 divide by x^4-4sinx
Similar expressions
y=8/x^4+4sinx

The derivative of the function/ y=8/x^4-4sinx

Derivative of y=8/x^4-4sinx

The solution

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8            
-- - 4*sin(x)
 4           
x

$$- 4 \sin{\left(x \right)} + \frac{8}{x^{4}}$$

d /8            \
--|-- - 4*sin(x)|
dx| 4           |
  \x            /

$$\frac{d}{d x} \left(- 4 \sin{\left(x \right)} + \frac{8}{x^{4}}\right)$$

Transform

Detail solution

Differentiate $- 4 \sin{\left(x \right)} + \frac{8}{x^{4}}$ 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: $- \frac{32}{x^{5}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. 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: $4 \cos{\left(x \right)}$
  So, the result is: $- 4 \cos{\left(x \right)}$
The result is: $- 4 \cos{\left(x \right)} - \frac{32}{x^{5}}$

The answer is:

$- 4 \cos{\left(x \right)} - \frac{32}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  32           
- -- - 4*cos(x)
   5           
  x

$$- 4 \cos{\left(x \right)} - \frac{32}{x^{5}}$$

Simplify

The second derivative [src]

  /40         \
4*|-- + sin(x)|
  | 6         |
  \x          /

$$4 \left(\sin{\left(x \right)} + \frac{40}{x^{6}}\right)$$

Simplify

The third derivative [src]

  /  240         \
4*|- --- + cos(x)|
  |    7         |
  \   x          /

$$4 \left(\cos{\left(x \right)} - \frac{240}{x^{7}}\right)$$

Simplify

The graph

Derivative of y=8/x^4-4sinx