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z^4+5z-iz
The derivative of the function/ z^4+5z-iz

Derivative of z^4+5z-iz

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

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The solution

You have entered [src] 
 4            
z  + 5*z - I*z
z4+5z−izz^{4} + 5 z - i z 
d / 4            \
--\z  + 5*z - I*z/
dz
ddz(z4+5z−iz)\frac{d}{d z} \left(z^{4} + 5 z - i z\right)
Transform
Detail solution

  1. Differentiate z4+5z−izz^{4} + 5 z - i z term by term:

    1. Apply the power rule: z4z^{4} goes to 4z34 z^{3}

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

      1. Apply the power rule: zz goes to 11

      So, the result is: 55

    3. 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. Apply the power rule: zz goes to 11

        So, the result is: ii

      So, the result is: −i- i

    The result is: 4z3+5−i4 z^{3} + 5 - i

The answer is:

4z3+5−i4 z^{3} + 5 - i

The graph
02468-8-6-4-2-10100.02-0.02
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3
5 - I + 4*z
4z3+5−i4 z^{3} + 5 - i
Simplify
The second derivative [src] 
    2
12*z
12z212 z^{2}
Simplify
The third derivative [src] 
24*z
24z24 z
Simplify
The graph
Derivative of z^4+5z-iz
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