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The derivative of the function/ ax^(-5)

Derivative of ax^(-5)

Function f() - derivative -N order at the point
v

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from to

Piecewise:

The solution

You have entered [src] 
a 
--
 5
x
ax5\frac{a}{x^{5}} 
d /a \
--|--|
dx| 5|
  \x /
∂∂xax5\frac{\partial}{\partial x} \frac{a}{x^{5}}
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the power rule: 1x5\frac{1}{x^{5}} goes to −5x6- \frac{5}{x^{6}}

    So, the result is: −5ax6- \frac{5 a}{x^{6}}

The answer is:

−5ax6- \frac{5 a}{x^{6}}

The first derivative [src] 
-5*a
----
  6 
 x
−5ax6- \frac{5 a}{x^{6}}
Simplify
The second derivative [src] 
30*a
----
  7 
 x
30ax7\frac{30 a}{x^{7}}
Simplify
The third derivative [src] 
-210*a
------
   8  
  x
−210ax8- \frac{210 a}{x^{8}}
Simplify
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