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Derivative of:
Derivative of x^3*(x^2-1)^2
Derivative of log((x+1)/(x-1))
Derivative of log(x+11)
Derivative of e^x-e^(3*x)
Identical expressions
exp^(three *x^ four)
exponent of to the power of (3 multiply by x to the power of 4)
exponent of to the power of (three multiply by x to the power of four)
exp(3*x4)
exp3*x4
exp^(3*x⁴)
exp^(3x^4)
exp(3x4)
exp3x4
exp^3x^4

The derivative of the function/ exp^(3*x^4)

Derivative of exp^(3*x^4)

The solution

You have entered [src]

    4
 3*x 
E

$$e^{3 x^{4}}$$

E^(3*x^4)

Detail solution

Let $u = 3 x^{4}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x^{4}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $12 x^{3}$
The result of the chain rule is:

$12 x^{3} e^{3 x^{4}}$

The answer is:

$12 x^{3} e^{3 x^{4}}$

The first derivative [src]

          4
    3  3*x 
12*x *e

$$12 x^{3} e^{3 x^{4}}$$

Simplify

The second derivative [src]

                     4
    2 /       4\  3*x 
36*x *\1 + 4*x /*e

$$36 x^{2} \left(4 x^{4} + 1\right) e^{3 x^{4}}$$

Simplify

The third derivative [src]

                             4
     /        4       8\  3*x 
72*x*\1 + 18*x  + 24*x /*e

$$72 x \left(24 x^{8} + 18 x^{4} + 1\right) e^{3 x^{4}}$$

Simplify