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Derivative of:
Derivative of e^(sin(1-3*x)^(2))
Derivative of x*e^((-1)/x^3)
Derivative of x^3-48x+17
Derivative of sin(t)*cos(t)
Identical expressions
(sqrt(three -4y))/cos5
( square root of (3 minus 4y)) divide by co sinus of e of 5
( square root of (three minus 4y)) divide by co sinus of e of 5
(√(3-4y))/cos5
sqrt3-4y/cos5
(sqrt(3-4y)) divide by cos5
Similar expressions
(sqrt(3+4y))/cos5

The derivative of the function/ (sqrt(3-4y))/cos5

Derivative of (sqrt(3-4y))/cos5

The solution

You have entered [src]

  _________
\/ 3 - 4*y 
-----------
   cos(5)

$$\frac{\sqrt{3 - 4 y}}{\cos{\left(5 \right)}}$$

sqrt(3 - 4*y)/cos(5)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 - 4 y$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(3 - 4 y\right)$ :
  1. Differentiate $3 - 4 y$ term by term:
    1. The derivative of the constant $3$ is zero.
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $y$ goes to $1$
      So, the result is: $-4$
    The result is: $-4$
  The result of the chain rule is:
  
  $- \frac{2}{\sqrt{3 - 4 y}}$
So, the result is: $- \frac{2}{\sqrt{3 - 4 y} \cos{\left(5 \right)}}$

The answer is:

$- \frac{2}{\sqrt{3 - 4 y} \cos{\left(5 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       -2         
------------------
  _________       
\/ 3 - 4*y *cos(5)

$$- \frac{2}{\sqrt{3 - 4 y} \cos{\left(5 \right)}}$$

Simplify

The second derivative [src]

        -4         
-------------------
         3/2       
(3 - 4*y)   *cos(5)

$$- \frac{4}{\left(3 - 4 y\right)^{\frac{3}{2}} \cos{\left(5 \right)}}$$

Simplify

The third derivative [src]

        -24        
-------------------
         5/2       
(3 - 4*y)   *cos(5)

$$- \frac{24}{\left(3 - 4 y\right)^{\frac{5}{2}} \cos{\left(5 \right)}}$$

Simplify