Mister Exam

Other calculators

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

Derivative of e^x-sinx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 x         
E  - sin(x)
ex−sin⁡(x)e^{x} - \sin{\left(x \right)} 
E^x - sin(x)
Detail solution

  1. Differentiate ex−sin⁡(x)e^{x} - \sin{\left(x \right)} term by term:

    1. The derivative of exe^{x} is itself.

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

        ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

      So, the result is: −cos⁡(x)- \cos{\left(x \right)}

    The result is: ex−cos⁡(x)e^{x} - \cos{\left(x \right)}

The answer is:

ex−cos⁡(x)e^{x} - \cos{\left(x \right)}

The graph
02468-8-6-4-2-1010-2500025000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x         
E  - cos(x)
ex−cos⁡(x)e^{x} - \cos{\left(x \right)}
Simplify
The second derivative [src] 
 x         
e  + sin(x)
ex+sin⁡(x)e^{x} + \sin{\left(x \right)}
Simplify
The third derivative [src] 
          x
cos(x) + e
ex+cos⁡(x)e^{x} + \cos{\left(x \right)}
Simplify
The graph
Derivative of e^x-sinx
    © Mister Exam – Calculator