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The derivative of the function/ 4sinx+lnx+3x

Derivative of 4sinx+lnx+3x

The solution

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4*sin(x) + log(x) + 3*x

$$3 x + \left(\log{\left(x \right)} + 4 \sin{\left(x \right)}\right)$$

4*sin(x) + log(x) + 3*x

Detail solution

Differentiate $3 x + \left(\log{\left(x \right)} + 4 \sin{\left(x \right)}\right)$ term by term:
1. Differentiate $\log{\left(x \right)} + 4 \sin{\left(x \right)}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $4 \cos{\left(x \right)}$
  2. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  The result is: $4 \cos{\left(x \right)} + \frac{1}{x}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $3$
The result is: $4 \cos{\left(x \right)} + 3 + \frac{1}{x}$

The answer is:

$4 \cos{\left(x \right)} + 3 + \frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1           
3 + - + 4*cos(x)
    x

$$4 \cos{\left(x \right)} + 3 + \frac{1}{x}$$

Simplify

The second derivative [src]

 /1            \
-|-- + 4*sin(x)|
 | 2           |
 \x            /

$$- (4 \sin{\left(x \right)} + \frac{1}{x^{2}})$$

Simplify

The third derivative [src]

  /1            \
2*|-- - 2*cos(x)|
  | 3           |
  \x            /

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

Simplify