Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^(7/6)
Derivative of e^x-7
Derivative of x*sin(3*x)
Derivative of (x^2+4)/x
Identical expressions
sinx-2x^ six -e^x
sinus of x minus 2x to the power of 6 minus e to the power of x
sinus of x minus 2x to the power of six minus e to the power of x
sinx-2x6-ex
sinx-2x⁶-e^x
Similar expressions
sinx+2x^6-e^x
sinx-2x^6+e^x

The derivative of the function/ sinx-2x^6-e^x

Derivative of sinx-2x^6-e^x

The solution

You have entered [src]

            6    x
sin(x) - 2*x  - E

$$- e^{x} + \left(- 2 x^{6} + \sin{\left(x \right)}\right)$$

sin(x) - 2*x^6 - E^x

Detail solution

Differentiate $- e^{x} + \left(- 2 x^{6} + \sin{\left(x \right)}\right)$ term by term:
1. Differentiate $- 2 x^{6} + \sin{\left(x \right)}$ term by term:
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
    So, the result is: $- 12 x^{5}$
  The result is: $- 12 x^{5} + \cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $e^{x}$ is itself.
  So, the result is: $- e^{x}$
The result is: $- 12 x^{5} - e^{x} + \cos{\left(x \right)}$

The answer is:

$- 12 x^{5} - e^{x} + \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x       5         
- e  - 12*x  + cos(x)

$$- 12 x^{5} - e^{x} + \cos{\left(x \right)}$$

Simplify

The second derivative [src]

 /    4    x         \
-\60*x  + e  + sin(x)/

$$- (60 x^{4} + e^{x} + \sin{\left(x \right)})$$

Simplify

The third derivative [src]

 /     3             x\
-\240*x  + cos(x) + e /

$$- (240 x^{3} + e^{x} + \cos{\left(x \right)})$$

Simplify