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Derivative of:
Derivative of -x/2
Derivative of x^sqrt(x)
Derivative of e^cot(x)
Derivative of 2^x*cos(x)
Identical expressions
y=-(x/ four)+5cosx
y equally minus (x divide by 4) plus 5 co sinus of e of x
y equally minus (x divide by four) plus 5 co sinus of e of x
y=-x/4+5cosx
y=-(x divide by 4)+5cosx
Similar expressions
y=-(x/4)-5cosx
y=-x/4+5cos(x)
y=-(x/4+)5cosx
y=+(x/4)+5cosx

The derivative of the function/ y=-(x/4)+5cosx

Derivative of y=-(x/4)+5cosx

The solution

You have entered [src]

  x           
- - + 5*cos(x)
  4

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

-x/4 + 5*cos(x)

Detail solution

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

The answer is:

$- 5 \sin{\left(x \right)} - \frac{1}{4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-1/4 - 5*sin(x)

$$- 5 \sin{\left(x \right)} - \frac{1}{4}$$

Simplify

The second derivative [src]

-5*cos(x)

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

Simplify

The third derivative [src]

5*sin(x)

$$5 \sin{\left(x \right)}$$

Simplify

The graph

Derivative of y=-(x/4)+5cosx