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y=lnx+5lgx
The derivative of the function/ y=lnx+5lgx

Derivative of y=lnx+5lgx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x) + 5*log(x)
log⁡(x)+5log⁡(x)\log{\left(x \right)} + 5 \log{\left(x \right)} 
log(x) + 5*log(x)
Detail solution

  1. Differentiate log⁡(x)+5log⁡(x)\log{\left(x \right)} + 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. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

      So, the result is: 5x\frac{5}{x}

    The result is: 6x\frac{6}{x}

The answer is:

6x\frac{6}{x}

The graph
02468-8-6-4-2-1010-100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
6
-
x
6x\frac{6}{x}
Simplify
The second derivative [src] 
-6 
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  2
 x
−6x2- \frac{6}{x^{2}}
Simplify
The third derivative [src] 
12
--
 3
x
12x3\frac{12}{x^{3}}
Simplify
The graph
Derivative of y=lnx+5lgx
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