Mister Exam

Derivative of 1/(y+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1  
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y + 5
1y+5\frac{1}{y + 5}
1/(y + 5)
Detail solution
  1. Let u=y+5u = y + 5.

  2. Apply the power rule: 1u\frac{1}{u} goes to 1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddy(y+5)\frac{d}{d y} \left(y + 5\right):

    1. Differentiate y+5y + 5 term by term:

      1. Apply the power rule: yy goes to 11

      2. The derivative of the constant 55 is zero.

      The result is: 11

    The result of the chain rule is:

    1(y+5)2- \frac{1}{\left(y + 5\right)^{2}}

  4. Now simplify:

    1(y+5)2- \frac{1}{\left(y + 5\right)^{2}}


The answer is:

1(y+5)2- \frac{1}{\left(y + 5\right)^{2}}

The graph
02468-8-6-4-2-1010-500500
The first derivative [src]
  -1    
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       2
(y + 5) 
1(y+5)2- \frac{1}{\left(y + 5\right)^{2}}
The second derivative [src]
   2    
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       3
(5 + y) 
2(y+5)3\frac{2}{\left(y + 5\right)^{3}}
The third derivative [src]
  -6    
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       4
(5 + y) 
6(y+5)4- \frac{6}{\left(y + 5\right)^{4}}