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The derivative of the function/ cosx+5x-4^x

Derivative of cosx+5x-4^x

The solution

You have entered [src]

                x
cos(x) + 5*x - 4

$$- 4^{x} + \left(5 x + \cos{\left(x \right)}\right)$$

cos(x) + 5*x - 4^x

Detail solution

Differentiate $- 4^{x} + \left(5 x + \cos{\left(x \right)}\right)$ term by term:
1. Differentiate $5 x + \cos{\left(x \right)}$ term by term:
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $5$
  The result is: $5 - \sin{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. $\frac{d}{d x} 4^{x} = 4^{x} \log{\left(4 \right)}$
  So, the result is: $- 4^{x} \log{\left(4 \right)}$
The result is: $- 4^{x} \log{\left(4 \right)} - \sin{\left(x \right)} + 5$
Now simplify:

$- \log{\left(4^{4^{x}} \right)} - \sin{\left(x \right)} + 5$

The answer is:

$- \log{\left(4^{4^{x}} \right)} - \sin{\left(x \right)} + 5$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              x       
5 - sin(x) - 4 *log(4)

$$- 4^{x} \log{\left(4 \right)} - \sin{\left(x \right)} + 5$$

Simplify

The second derivative [src]

 / x    2            \
-\4 *log (4) + cos(x)/

$$- (4^{x} \log{\left(4 \right)}^{2} + \cos{\left(x \right)})$$

Simplify

The third derivative [src]

   x    3            
- 4 *log (4) + sin(x)

$$- 4^{x} \log{\left(4 \right)}^{3} + \sin{\left(x \right)}$$

Simplify