Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of f(x)=x^2
Derivative of x×ln(x)
Derivative of x^4+4*x^3-8*x^2-5
Derivative of -(x^2+289)/x
Identical expressions
(seven *x- five)^ four + one / seven ^ five *sqrt(x^ two)+sqrt(five *x)
(7 multiply by x minus 5) to the power of 4 plus 1 divide by 7 to the power of 5 multiply by square root of (x squared ) plus square root of (5 multiply by x)
(seven multiply by x minus five) to the power of four plus one divide by seven to the power of five multiply by square root of (x to the power of two) plus square root of (five multiply by x)
(7*x-5)^4+1/7^5*√(x^2)+√(5*x)
(7*x-5)4+1/75*sqrt(x2)+sqrt(5*x)
7*x-54+1/75*sqrtx2+sqrt5*x
(7*x-5)⁴+1/7⁵*sqrt(x²)+sqrt(5*x)
(7*x-5) to the power of 4+1/7 to the power of 5*sqrt(x to the power of 2)+sqrt(5*x)
(7x-5)^4+1/7^5sqrt(x^2)+sqrt(5x)
(7x-5)4+1/75sqrt(x2)+sqrt(5x)
7x-54+1/75sqrtx2+sqrt5x
7x-5^4+1/7^5sqrtx^2+sqrt5x
(7*x-5)^4+1 divide by 7^5*sqrt(x^2)+sqrt(5*x)
Similar expressions
(7*x-5)^4-1/7^5*sqrt(x^2)+sqrt(5*x)
(7*x-5)^4+1/7^5*sqrt(x^2)-sqrt(5*x)
(7*x+5)^4+1/7^5*sqrt(x^2)+sqrt(5*x)

The derivative of the function/ (7*x-5)^4+1/7^5*sqrt(x^2)+sqrt(5*x)

Derivative of (7x-5)^4+1/7^5sqrt(x^2)+sqrt(5*x)

The solution

You have entered [src]

                   ____          
         4   1    /  2      _____
(7*x - 5)  + --*\/  x   + \/ 5*x 
              5                  
             7

$$\sqrt{5 x} + \left(\left(7 x - 5\right)^{4} + \frac{\sqrt{x^{2}}}{16807}\right)$$

(7*x - 5)^4 + (1/7)^5*sqrt(x^2) + sqrt(5*x)

Detail solution

Differentiate $\sqrt{5 x} + \left(\left(7 x - 5\right)^{4} + \frac{\sqrt{x^{2}}}{16807}\right)$ term by term:
1. Differentiate $\left(7 x - 5\right)^{4} + \frac{\sqrt{x^{2}}}{16807}$ term by term:
  1. Let $u = 7 x - 5$ .
  2. Apply the power rule: $u^{4}$ goes to $4 u^{3}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 x - 5\right)$ :
    1. Differentiate $7 x - 5$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $7$
      2. The derivative of the constant $-5$ is zero.
      The result is: $7$
    The result of the chain rule is:
    
    $28 \left(7 x - 5\right)^{3}$
  4. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = x^{2}$ .
    2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      The result of the chain rule is:
      
      $\frac{x}{\left|{x}\right|}$
    So, the result is: $\frac{x}{16807 \left|{x}\right|}$
  The result is: $\frac{x}{16807 \left|{x}\right|} + 28 \left(7 x - 5\right)^{3}$
2. Let $u = 5 x$ .
3. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
  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: $5$
  The result of the chain rule is:
  
  $\frac{\sqrt{5}}{2 \sqrt{x}}$
The result is: $\frac{x}{16807 \left|{x}\right|} + 28 \left(7 x - 5\right)^{3} + \frac{\sqrt{5}}{2 \sqrt{x}}$
Now simplify:

$\frac{x}{16807 \left|{x}\right|} + 28 \left(7 x - 5\right)^{3} + \frac{\sqrt{5}}{2 \sqrt{x}}$

The answer is:

$\frac{x}{16807 \left|{x}\right|} + 28 \left(7 x - 5\right)^{3} + \frac{\sqrt{5}}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                  ___   ___          
            3   \/ 5 *\/ x      |x|  
28*(7*x - 5)  + ----------- + -------
                    2*x       16807*x

$$28 \left(7 x - 5\right)^{3} + \frac{\sqrt{5} \sqrt{x}}{2 x} + \frac{\left|{x}\right|}{16807 x}$$

Simplify

The second derivative [src]

                    ___                      
              2   \/ 5       |x|      sign(x)
588*(-5 + 7*x)  - ------ - -------- + -------
                     3/2          2   16807*x
                  4*x      16807*x

$$588 \left(7 x - 5\right)^{2} + \frac{\operatorname{sign}{\left(x \right)}}{16807 x} - \frac{\left|{x}\right|}{16807 x^{2}} - \frac{\sqrt{5}}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

                                                                ___
                   2*sign(x)   2*DiracDelta(x)    2*|x|     3*\/ 5 
-41160 + 57624*x - --------- + --------------- + -------- + -------
                           2       16807*x              3       5/2
                    16807*x                      16807*x     8*x

$$57624 x - 41160 + \frac{2 \delta\left(x\right)}{16807 x} - \frac{2 \operatorname{sign}{\left(x \right)}}{16807 x^{2}} + \frac{2 \left|{x}\right|}{16807 x^{3}} + \frac{3 \sqrt{5}}{8 x^{\frac{5}{2}}}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (7x-5)^4+1/7^5sqrt(x^2)+sqrt(5*x)

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (7*x-5)^4+1/7^5*sqrt(x^2)+sqrt(5*x)

The graph:

Piecewise:

The solution

Derivative of (7x-5)^4+1/7^5sqrt(x^2)+sqrt(5*x)