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y=2x^3-5x^2+7x+4

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Derivative of:
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Identical expressions
y= two x^ three -5x^2+7x+ four
y equally 2x cubed minus 5x squared plus 7x plus 4
y equally two x to the power of three minus 5x squared plus 7x plus four
y=2x3-5x2+7x+4
y=2x³-5x²+7x+4
y=2x to the power of 3-5x to the power of 2+7x+4
Similar expressions
y=2x^3-5x^2-7x+4
y=2x^3-5x^2+7x-4
y=2x^3+5x^2+7x+4

The derivative of the function/ y=2x^3-5x^2+7x+4

Derivative of y=2x^3-5x^2+7x+4

The solution

You have entered [src]

   3      2          
2*x  - 5*x  + 7*x + 4

$$2 x^{3} - 5 x^{2} + 7 x + 4$$

d /   3      2          \
--\2*x  - 5*x  + 7*x + 4/
dx

$$\frac{d}{d x} \left(2 x^{3} - 5 x^{2} + 7 x + 4\right)$$

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Detail solution

Differentiate $2 x^{3} - 5 x^{2} + 7 x + 4$ 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: $6 x^{2}$
2. 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: $x^{2}$ goes to $2 x$
    So, the result is: $10 x$
  So, the result is: $- 10 x$
3. 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: $7$
4. The derivative of the constant $4$ is zero.
The result is: $6 x^{2} - 10 x + 7$

The answer is:

$6 x^{2} - 10 x + 7$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              2
7 - 10*x + 6*x

$$6 x^{2} - 10 x + 7$$

Simplify

The second derivative [src]

2*(-5 + 6*x)

$$2 \cdot \left(6 x - 5\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify

The graph

Derivative of y=2x^3-5x^2+7x+4