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Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Derivative of (2*x^2-6*x-7)/3
Identical expressions
4x^ two -7x^ ten +ln10x
4x squared minus 7x to the power of 10 plus ln10x
4x to the power of two minus 7x to the power of ten plus ln10x
4x2-7x10+ln10x
4x²-7x^10+ln10x
4x to the power of 2-7x to the power of 10+ln10x
Similar expressions
4x^2+7x^10+ln10x
4x^2-7x^10-ln10x

The derivative of the function/ 4x^2-7x^10+ln10x

Derivative of 4x^2-7x^10+ln10x

The solution

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   2      10            
4*x  - 7*x   + log(10*x)

$$\left(- 7 x^{10} + 4 x^{2}\right) + \log{\left(10 x \right)}$$

4*x^2 - 7*x^10 + log(10*x)

Detail solution

Differentiate $\left(- 7 x^{10} + 4 x^{2}\right) + \log{\left(10 x \right)}$ term by term:
1. Differentiate $- 7 x^{10} + 4 x^{2}$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $8 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{10}$ goes to $10 x^{9}$
    So, the result is: $- 70 x^{9}$
  The result is: $- 70 x^{9} + 8 x$
2. Let $u = 10 x$ .
3. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} 10 x$ :
  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: $10$
  The result of the chain rule is:
  
  $\frac{1}{x}$
The result is: $- 70 x^{9} + 8 x + \frac{1}{x}$

The answer is:

$- 70 x^{9} + 8 x + \frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1       9      
- - 70*x  + 8*x
x

$$- 70 x^{9} + 8 x + \frac{1}{x}$$

Simplify

The second derivative [src]

    1         8
8 - -- - 630*x 
     2         
    x

$$- 630 x^{8} + 8 - \frac{1}{x^{2}}$$

Simplify

The third derivative [src]

  /1          7\
2*|-- - 2520*x |
  | 3          |
  \x           /

$$2 \left(- 2520 x^{7} + \frac{1}{x^{3}}\right)$$

Simplify