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Derivative of:
Derivative of atan(sqrt(x))
Derivative of 3*x^5
Derivative of 3*x^2*e^x
Derivative of 3*cos(3*x)
Graphing y =:
3*x^2*e^x
Identical expressions
three *x^ two *e^x
3 multiply by x squared multiply by e to the power of x
three multiply by x to the power of two multiply by e to the power of x
3*x2*ex
3*x²*e^x
3*x to the power of 2*e to the power of x
3x^2e^x
3x2ex

The derivative of the function/ 3*x^2*e^x

Derivative of 3x^2e^x

The solution

You have entered [src]

   2  x
3*x *E

$$e^{x} 3 x^{2}$$

(3*x^2)*E^x

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = 3 x^{2}$ ; 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: $x^{2}$ goes to $2 x$
  So, the result is: $6 x$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $3 x^{2} e^{x} + 6 x e^{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2  x        x
3*x *e  + 6*x*e

$$3 x^{2} e^{x} + 6 x e^{x}$$

Simplify

The second derivative [src]

  /     2      \  x
3*\2 + x  + 4*x/*e

$$3 \left(x^{2} + 4 x + 2\right) e^{x}$$

Simplify

The third derivative [src]

  /     2      \  x
3*\6 + x  + 6*x/*e

$$3 \left(x^{2} + 6 x + 6\right) e^{x}$$

Simplify

The graph

Derivative of 3*x^2*e^x