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y=lnx-2x^2
The derivative of the function/ y=lnx-2x^2

Derivative of y=lnx-2x^2

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

You have entered [src] 
            2
log(x) - 2*x
−2x2+log⁡(x)- 2 x^{2} + \log{\left(x \right)} 
log(x) - 2*x^2
Detail solution

  1. Differentiate −2x2+log⁡(x)- 2 x^{2} + \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: x2x^{2} goes to 2x2 x

      So, the result is: −4x- 4 x

    The result is: −4x+1x- 4 x + \frac{1}{x}

The answer is:

−4x+1x- 4 x + \frac{1}{x}

The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1      
- - 4*x
x
−4x+1x- 4 x + \frac{1}{x}
Simplify
The second derivative [src] 
 /    1 \
-|4 + --|
 |     2|
 \    x /
−(4+1x2)- (4 + \frac{1}{x^{2}})
Simplify
The third derivative [src] 
2 
--
 3
x
2x3\frac{2}{x^{3}}
Simplify
The graph
Derivative of y=lnx-2x^2
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