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Identical expressions
e^x*sinx- one
e to the power of x multiply by sinus of x minus 1
e to the power of x multiply by sinus of x minus one
ex*sinx-1
e^xsinx-1
exsinx-1
Similar expressions
e^x*sinx+1

The derivative of the function/ e^x*sinx-1

Derivative of e^x*sinx-1

The solution

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 x           
e *sin(x) - 1

$$e^{x} \sin{\left(x \right)} - 1$$

d / x           \
--\e *sin(x) - 1/
dx

$$\frac{d}{d x} \left(e^{x} \sin{\left(x \right)} - 1\right)$$

Transform

Detail solution

Differentiate $e^{x} \sin{\left(x \right)} - 1$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of $e^{x}$ is itself.
  $g{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result is: $e^{x} \sin{\left(x \right)} + e^{x} \cos{\left(x \right)}$
2. The derivative of the constant $\left(-1\right) 1$ is zero.
The result is: $e^{x} \sin{\left(x \right)} + e^{x} \cos{\left(x \right)}$
Now simplify:

$\sqrt{2} e^{x} \sin{\left(x + \frac{\pi}{4} \right)}$

The answer is:

$\sqrt{2} e^{x} \sin{\left(x + \frac{\pi}{4} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        x    x       
cos(x)*e  + e *sin(x)

$$e^{x} \sin{\left(x \right)} + e^{x} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

          x
2*cos(x)*e

$$2 e^{x} \cos{\left(x \right)}$$

Simplify

The third derivative [src]

                      x
2*(-sin(x) + cos(x))*e

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

Simplify

The graph

Derivative of e^x*sinx-1