Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^3*lnx
Derivative of x^4*e^x
Derivative of (1/x)^x
Derivative of log(11*x)
Identical expressions
two ^(three *x+ four)
2 to the power of (3 multiply by x plus 4)
two to the power of (three multiply by x plus four)
2(3*x+4)
23*x+4
2^(3x+4)
2(3x+4)
23x+4
2^3x+4
Similar expressions
2^(3*x-4)

The derivative of the function/ 2^(3*x+4)

Derivative of 2^(3*x+4)

The solution

You have entered [src]

 3*x + 4
2

$$2^{3 x + 4}$$

2^(3*x + 4)

Detail solution

Let $u = 3 x + 4$ .
$\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 4\right)$ :
1. Differentiate $3 x + 4$ 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: $3$
  2. The derivative of the constant $4$ is zero.
  The result is: $3$
The result of the chain rule is:

$3 \cdot 2^{3 x + 4} \log{\left(2 \right)}$
Now simplify:

$48 \cdot 2^{3 x} \log{\left(2 \right)}$

The answer is:

$48 \cdot 2^{3 x} \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3*x + 4       
3*2       *log(2)

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

Simplify

The second derivative [src]

     3*x    2   
144*2   *log (2)

$$144 \cdot 2^{3 x} \log{\left(2 \right)}^{2}$$

Simplify

The third derivative [src]

     3*x    3   
432*2   *log (2)

$$432 \cdot 2^{3 x} \log{\left(2 \right)}^{3}$$

Simplify