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Derivative of:
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Derivative of (5*x-6)*cos(x)-5*sin(x)-8
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Identical expressions
y=sin(x)-x^ six
y equally sinus of (x) minus x to the power of 6
y equally sinus of (x) minus x to the power of six
y=sin(x)-x6
y=sinx-x6
y=sin(x)-x⁶
y=sinx-x^6
Similar expressions
y=sin(x)+x^6
y=sinx-x^6

The derivative of the function/ y=sin(x)-x^6

Derivative of y=sin(x)-x^6

The solution

You have entered [src]

          6
sin(x) - x

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

Transform

Detail solution

Differentiate $- x^{6} + \sin{\left(x \right)}$ term by term:
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
  So, the result is: $- 6 x^{5}$
The result is: $- 6 x^{5} + \cos{\left(x \right)}$

The answer is:

$- 6 x^{5} + \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     5         
- 6*x  + cos(x)

$$- 6 x^{5} + \cos{\left(x \right)}$$

Simplify

The second derivative [src]

 /    4         \
-\30*x  + sin(x)/

$$- (30 x^{4} + \sin{\left(x \right)})$$

Simplify

The third derivative [src]

 /     3         \
-\120*x  + cos(x)/

$$- (120 x^{3} + \cos{\left(x \right)})$$

Simplify

The graph

Derivative of y=sin(x)-x^6