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Derivative of:
Derivative of (sin(x))^2
Derivative of x-1
Derivative of sin(x)+cos(x)
Derivative of asin(x)
Identical expressions
y=(sinx)+ six - six ^x
y equally ( sinus of x) plus 6 minus 6 to the power of x
y equally ( sinus of x) plus six minus six to the power of x
y=(sinx)+6-6x
y=sinx+6-6x
y=sinx+6-6^x
Similar expressions
y=(sinx)+6+6^x
y=(sinx)-6-6^x

The derivative of the function/ y=(sinx)+6-6^x

Derivative of y=(sinx)+6-6^x

The solution

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              x
sin(x) + 6 - 6

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

sin(x) + 6 - 6^x

Detail solution

Differentiate $- 6^{x} + \left(\sin{\left(x \right)} + 6\right)$ term by term:
1. Differentiate $\sin{\left(x \right)} + 6$ 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 the constant $6$ is zero.
  The result is: $\cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. $\frac{d}{d x} 6^{x} = 6^{x} \log{\left(6 \right)}$
  So, the result is: $- 6^{x} \log{\left(6 \right)}$
The result is: $- 6^{x} \log{\left(6 \right)} + \cos{\left(x \right)}$

The answer is:

$- 6^{x} \log{\left(6 \right)} + \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x                
- 6 *log(6) + cos(x)

$$- 6^{x} \log{\left(6 \right)} + \cos{\left(x \right)}$$

Simplify

The second derivative [src]

 / x    2            \
-\6 *log (6) + sin(x)/

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

Simplify

The third derivative [src]

 / x    3            \
-\6 *log (6) + cos(x)/

$$- (6^{x} \log{\left(6 \right)}^{3} + \cos{\left(x \right)})$$

Simplify

The graph

Derivative of y=(sinx)+6-6^x