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The derivative of the function/ y=5e^x-3lnx

Derivative of y=5e^x-3lnx

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
   x           
5*E  - 3*log(x)
5ex−3log⁡(x)5 e^{x} - 3 \log{\left(x \right)} 
5*E^x - 3*log(x)
Detail solution

  1. Differentiate 5ex−3log⁡(x)5 e^{x} - 3 \log{\left(x \right)} term by term:

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

      1. The derivative of exe^{x} is itself.

      So, the result is: 5ex5 e^{x}

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

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

      So, the result is: −3x- \frac{3}{x}

    The result is: 5ex−3x5 e^{x} - \frac{3}{x}

The answer is:

5ex−3x5 e^{x} - \frac{3}{x}

The graph
02468-8-6-4-2-1010200000-100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  3      x
- - + 5*e 
  x
5ex−3x5 e^{x} - \frac{3}{x}
Simplify
The second derivative [src] 
3       x
-- + 5*e 
 2       
x
5ex+3x25 e^{x} + \frac{3}{x^{2}}
Simplify
The third derivative [src] 
  6       x
- -- + 5*e 
   3       
  x
5ex−6x35 e^{x} - \frac{6}{x^{3}}
Simplify
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