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y=lnx+4x^5
The derivative of the function/ y=lnx+4x^5

Derivative of y=lnx+4x^5

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

The graph:

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The solution

You have entered [src] 
            5
log(x) + 4*x
4x5+log⁡(x)4 x^{5} + \log{\left(x \right)} 
d /            5\
--\log(x) + 4*x /
dx
ddx(4x5+log⁡(x))\frac{d}{d x} \left(4 x^{5} + \log{\left(x \right)}\right)
Transform
Detail solution

  1. Differentiate 4x5+log⁡(x)4 x^{5} + \log{\left(x \right)} term by term:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

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

      1. Apply the power rule: x5x^{5} goes to 5x45 x^{4}

      So, the result is: 20x420 x^{4}

    The result is: 20x4+1x20 x^{4} + \frac{1}{x}

  2. Now simplify:

    20x5+1x\frac{20 x^{5} + 1}{x}

The answer is:

20x5+1x\frac{20 x^{5} + 1}{x}

The graph
02468-8-6-4-2-1010-500000500000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1       4
- + 20*x 
x
20x4+1x20 x^{4} + \frac{1}{x}
Simplify
The second derivative [src] 
  1        3
- -- + 80*x 
   2        
  x
80x3−1x280 x^{3} - \frac{1}{x^{2}}
Simplify
The third derivative [src] 
  /1         2\
2*|-- + 120*x |
  | 3         |
  \x          /
2⋅(120x2+1x3)2 \cdot \left(120 x^{2} + \frac{1}{x^{3}}\right)
Simplify
The graph
Derivative of y=lnx+4x^5
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