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Identical expressions
10x^ three +2cosx
10x cubed plus 2 co sinus of e of x
10x to the power of three plus 2 co sinus of e of x
10x3+2cosx
10x³+2cosx
10x to the power of 3+2cosx
Similar expressions
10x^3-2cosx

The derivative of the function/ 10x^3+2cosx

Derivative of 10x^3+2cosx

The solution

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    3           
10*x  + 2*cos(x)

$$10 x^{3} + 2 \cos{\left(x \right)}$$

d /    3           \
--\10*x  + 2*cos(x)/
dx

$$\frac{d}{d x} \left(10 x^{3} + 2 \cos{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $10 x^{3} + 2 \cos{\left(x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $30 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $- 2 \sin{\left(x \right)}$
The result is: $30 x^{2} - 2 \sin{\left(x \right)}$

The answer is:

$30 x^{2} - 2 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                2
-2*sin(x) + 30*x

$$30 x^{2} - 2 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

2*(-cos(x) + 30*x)

$$2 \cdot \left(30 x - \cos{\left(x \right)}\right)$$

Simplify

The third derivative [src]

2*(30 + sin(x))

$$2 \left(\sin{\left(x \right)} + 30\right)$$

Simplify

The graph

Derivative of 10x^3+2cosx