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Derivative of:
Derivative of 2x²
Derivative of x^2*sqrt(1-x^2)
Derivative of 2*sqrt(x^3)
Derivative of (x+1)*(x+2)^2*(x+3)^3
Identical expressions
y=sqrt(four - five *x)
y equally square root of (4 minus 5 multiply by x)
y equally square root of (four minus five multiply by x)
y=√(4-5*x)
y=sqrt(4-5x)
y=sqrt4-5x
Similar expressions
y=sqrt(4+5*x)

The derivative of the function/ y=sqrt(4-5*x)

Derivative of y=sqrt(4-5*x)

The solution

You have entered [src]

  _________
\/ 4 - 5*x

$$\sqrt{4 - 5 x}$$

sqrt(4 - 5*x)

Detail solution

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

$- \frac{5}{2 \sqrt{4 - 5 x}}$

The answer is:

$- \frac{5}{2 \sqrt{4 - 5 x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     -5      
-------------
    _________
2*\/ 4 - 5*x

$$- \frac{5}{2 \sqrt{4 - 5 x}}$$

Simplify

The second derivative [src]

     -25      
--------------
           3/2
4*(4 - 5*x)

$$- \frac{25}{4 \left(4 - 5 x\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

    -375      
--------------
           5/2
8*(4 - 5*x)

$$- \frac{375}{8 \left(4 - 5 x\right)^{\frac{5}{2}}}$$

Simplify

3-я производная [src]

    -375      
--------------
           5/2
8*(4 - 5*x)

$$- \frac{375}{8 \left(4 - 5 x\right)^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of y=sqrt(4-5*x)