Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of log(cos(x))
Derivative of y=2x^3-5x^2+7x+4
Derivative of cos^3(6x)
Derivative of cos(1-4x)
Integral of d{x}:
x^4+4x^3
Graphing y =:
x^4+4x^3
Identical expressions
y=x^ four +4x^ three
y equally x to the power of 4 plus 4x cubed
y equally x to the power of four plus 4x to the power of three
y=x4+4x3
y=x⁴+4x³
y=x to the power of 4+4x to the power of 3
Similar expressions
y=x^4-4x^3
y(x)=x^4+4x^3-8x^2

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

Derivative of y=x^4+4x^3

The solution

You have entered [src]

 4      3
x  + 4*x

$$x^{4} + 4 x^{3}$$

x^4 + 4*x^3

Detail solution

Differentiate $x^{4} + 4 x^{3}$ term by term:
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
2. 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: $12 x^{2}$
The result is: $4 x^{3} + 12 x^{2}$
Now simplify:

$4 x^{2} \left(x + 3\right)$

The answer is:

$4 x^{2} \left(x + 3\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3       2
4*x  + 12*x

$$4 x^{3} + 12 x^{2}$$

Simplify

The second derivative [src]

12*x*(2 + x)

$$12 x \left(x + 2\right)$$

Simplify

The third derivative [src]

24*(1 + x)

$$24 \left(x + 1\right)$$

Simplify

The graph

Derivative of y=x^4+4x^3