Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x*sqrt(x)
Derivative of (x^3)/3
Derivative of arccos(3x+1)
Derivative of 2x-3x^2
Identical expressions
y=sin(8x)+ two ^x
y equally sinus of (8x) plus 2 to the power of x
y equally sinus of (8x) plus two to the power of x
y=sin(8x)+2x
y=sin8x+2x
y=sin8x+2^x
Similar expressions
y=sin(8x)-2^x

The derivative of the function/ y=sin(8x)+2^x

Derivative of y=sin(8x)+2^x

The solution

You have entered [src]

            x
sin(8*x) + 2

$$2^{x} + \sin{\left(8 x \right)}$$

sin(8*x) + 2^x

Detail solution

Differentiate $2^{x} + \sin{\left(8 x \right)}$ term by term:
1. Let $u = 8 x$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 8 x$ :
  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: $8$
  The result of the chain rule is:
  
  $8 \cos{\left(8 x \right)}$
4. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
The result is: $2^{x} \log{\left(2 \right)} + 8 \cos{\left(8 x \right)}$

The answer is:

$2^{x} \log{\left(2 \right)} + 8 \cos{\left(8 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              x       
8*cos(8*x) + 2 *log(2)

$$2^{x} \log{\left(2 \right)} + 8 \cos{\left(8 x \right)}$$

Simplify

The second derivative [src]

                x    2   
-64*sin(8*x) + 2 *log (2)

$$2^{x} \log{\left(2 \right)}^{2} - 64 \sin{\left(8 x \right)}$$

Simplify

The third derivative [src]

                 x    3   
-512*cos(8*x) + 2 *log (2)

$$2^{x} \log{\left(2 \right)}^{3} - 512 \cos{\left(8 x \right)}$$

Simplify

The graph

Derivative of y=sin(8x)+2^x