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Derivative of:
Derivative of sin(x)/cos(x)
Derivative of cos(x)^(3)
Derivative of 1/(2*sqrt(x))
Derivative of x^5*sin(x)
Identical expressions
e^(six *x- two)
e to the power of (6 multiply by x minus 2)
e to the power of (six multiply by x minus two)
e(6*x-2)
e6*x-2
e^(6x-2)
e(6x-2)
e6x-2
e^6x-2
Similar expressions
e^(6*x+2)

The derivative of the function/ e^(6*x-2)

Derivative of e^(6*x-2)

The solution

You have entered [src]

 6*x - 2
e

e^{6 x - 2}

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

\frac{d}{d x} e^{6 x - 2}

Transform

Detail solution

Let $u = 6 x - 2$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(6 x - 2\right)$ :
1. Differentiate $6 x - 2$ 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: $x$ goes to $1$
    So, the result is: $6$
  2. The derivative of the constant $\left(-1\right) 2$ is zero.
  The result is: $6$
The result of the chain rule is:

$6 e^{6 x - 2}$
Now simplify:

$6 e^{6 x - 2}$

The answer is:

6 e^{6 x - 2}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   6*x - 2
6*e

6 e^{6 x - 2}

Simplify

The second derivative [src]

    -2 + 6*x
36*e

36 e^{6 x - 2}

Simplify

The third derivative [src]

     -2 + 6*x
216*e

216 e^{6 x - 2}

Simplify

The graph

Derivative of e^(6*x-2)