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y=x^4+3x^3–7x^2+x+2
The derivative of the function/ y=x^4+3x^3–7x^2+x+2

Derivative of y=x^4+3x^3–7x^2+x+2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 4      3      2        
x  + 3*x  - 7*x  + x + 2
$$x^{4} + 3 x^{3} - 7 x^{2} + x + 2$$ 
d / 4      3      2        \
--\x  + 3*x  - 7*x  + x + 2/
dx
$$\frac{d}{d x} \left(x^{4} + 3 x^{3} - 7 x^{2} + x + 2\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. 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:

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

      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:

      So, the result is:

    4. Apply the power rule: goes to

    5. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              3      2
1 - 14*x + 4*x  + 9*x
$$4 x^{3} + 9 x^{2} - 14 x + 1$$
Simplify
The second derivative [src] 
  /        2      \
2*\-7 + 6*x  + 9*x/
$$2 \cdot \left(6 x^{2} + 9 x - 7\right)$$
Simplify
3-th derivative [src] 
6*(3 + 4*x)
$$6 \cdot \left(4 x + 3\right)$$
Simplify
The third derivative [src] 
6*(3 + 4*x)
$$6 \cdot \left(4 x + 3\right)$$
Simplify
The graph
Derivative of y=x^4+3x^3–7x^2+x+2
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