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Derivative of:
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Identical expressions
3x^ four - two x^2+ five
3x to the power of 4 minus 2x squared plus 5
3x to the power of four minus two x squared plus five
3x4-2x2+5
3x⁴-2x²+5
3x to the power of 4-2x to the power of 2+5
Similar expressions
3x^4-2x^2-5
3x^4+2x^2+5

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

Derivative of 3x^4-2x^2+5

The solution

You have entered [src]

   4      2    
3*x  - 2*x  + 5

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

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

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

Transform

Detail solution

Differentiate $3 x^{4} - 2 x^{2} + 5$ 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: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $12 x^{3}$
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: $4 x$
  So, the result is: $- 4 x$
3. The derivative of the constant $5$ is zero.
The result is: $12 x^{3} - 4 x$

The answer is:

$12 x^{3} - 4 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
-4*x + 12*x

$$12 x^{3} - 4 x$$

Simplify

The second derivative [src]

  /        2\
4*\-1 + 9*x /

$$4 \cdot \left(9 x^{2} - 1\right)$$

Simplify

The third derivative [src]

72*x

$$72 x$$

Simplify

The graph

Derivative of 3x^4-2x^2+5