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y=log5x+3x^4

Derivative of y=log5x+3x^4

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
              4
log(5*x) + 3*x 
$$3 x^{4} + \log{\left(5 x \right)}$$
d /              4\
--\log(5*x) + 3*x /
dx                 
$$\frac{d}{d x} \left(3 x^{4} + \log{\left(5 x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
1       3
- + 12*x 
x        
$$12 x^{3} + \frac{1}{x}$$
The second derivative [src]
  1        2
- -- + 36*x 
   2        
  x         
$$36 x^{2} - \frac{1}{x^{2}}$$
The third derivative [src]
  /1        \
2*|-- + 36*x|
  | 3       |
  \x        /
$$2 \cdot \left(36 x + \frac{1}{x^{3}}\right)$$
The graph
Derivative of y=log5x+3x^4