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Derivative of:
Derivative of (x-1)^3
Derivative of x^3+4
Derivative of x^3-3*x+1
Derivative of sin(pi*x)
Identical expressions
y=e^3x^ two -6x
y equally e cubed x squared minus 6x
y equally e cubed x to the power of two minus 6x
y=e3x2-6x
y=e³x²-6x
y=e to the power of 3x to the power of 2-6x
Similar expressions
y=e^3x^2+6x
What you mean?
e^3*x^2 - 6*x
e^((3*x)^2) - 6*x
e^((3*x)^2) - 6*x

The derivative of the function/ y=e^3x^2-6x

You entered:

y=e^3x^2-6x

What you mean?

e^3*x^2 - 6*x

e^((3*x)^2) - 6*x

e^((3*x)^2) - 6*x

Derivative of y=e^3x^2-6x

The solution

You have entered [src]

 3  2      
e *x  - 6*x

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

d / 3  2      \
--\e *x  - 6*x/
dx

$$\frac{d}{d x} \left(x^{2} e^{3} - 6 x\right)$$

Transform

Detail solution

Differentiate $x^{2} e^{3} - 6 x$ term by term:
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: $2 x e^{3}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  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: $6$
  So, the result is: $-6$
The result is: $2 x e^{3} - 6$

The answer is:

$2 x e^{3} - 6$

The graph

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The first derivative [src]

          3
-6 + 2*x*e

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

Simplify

The second derivative [src]

   3
2*e

$$2 e^{3}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of y=e^3x^2-6x