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y=e^2x*(lnx+x^2)

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Derivative of:
Derivative of x^-(4/5)
Derivative of ln(x^2-2x)
Derivative of 2*x-x^2
Derivative of 2^x*x^2
Identical expressions
y=e^ two x*(lnx+x^2)
y equally e squared x multiply by (lnx plus x squared )
y equally e to the power of two x multiply by (lnx plus x squared )
y=e2x*(lnx+x2)
y=e2x*lnx+x2
y=e²x*(lnx+x²)
y=e to the power of 2x*(lnx+x to the power of 2)
y=e^2x(lnx+x^2)
y=e2x(lnx+x2)
y=e2xlnx+x2
y=e^2xlnx+x^2
Similar expressions
y=e^2x*(lnx-x^2)

The derivative of the function/ y=e^2x*(lnx+x^2)

Derivative of y=e^2x*(lnx+x^2)

The solution

You have entered [src]

 2   /          2\
E *x*\log(x) + x /

$$e^{2} x \left(x^{2} + \log{\left(x \right)}\right)$$

(E^2*x)*(log(x) + x^2)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = e^{2} x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $e^{2}$
$g{\left(x \right)} = x^{2} + \log{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} + \log{\left(x \right)}$ term by term:
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x + \frac{1}{x}$
The result is: $x \left(2 x + \frac{1}{x}\right) e^{2} + \left(x^{2} + \log{\left(x \right)}\right) e^{2}$
Now simplify:

$\left(3 x^{2} + \log{\left(x \right)} + 1\right) e^{2}$

The answer is:

$\left(3 x^{2} + \log{\left(x \right)} + 1\right) e^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/          2\  2     /1      \  2
\log(x) + x /*e  + x*|- + 2*x|*e 
                     \x      /

$$x \left(2 x + \frac{1}{x}\right) e^{2} + \left(x^{2} + \log{\left(x \right)}\right) e^{2}$$

Simplify

The second derivative [src]

/2           /    1 \\  2
|- + 4*x + x*|2 - --||*e 
|x           |     2||   
\            \    x //

$$\left(x \left(2 - \frac{1}{x^{2}}\right) + 4 x + \frac{2}{x}\right) e^{2}$$

Simplify

The third derivative [src]

/    1 \  2
|6 - --|*e 
|     2|   
\    x /

$$\left(6 - \frac{1}{x^{2}}\right) e^{2}$$

Simplify

The graph

Derivative of y=e^2x*(lnx+x^2)