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Derivative of:
Derivative of arctg(1/x)
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Derivative of cot(1/x)
Graphing y =:
x^3+6x^2
Plot:
x^3+6x^2
Identical expressions
y=x^ three +6x^ two
y equally x cubed plus 6x squared
y equally x to the power of three plus 6x to the power of two
y=x3+6x2
y=x³+6x²
y=x to the power of 3+6x to the power of 2
Similar expressions
(x^3+6*x^2)/sqrt(3)
y=x^3-6x^2

The derivative of the function/ y=x^3+6x^2

Derivative of y=x^3+6x^2

The solution

You have entered [src]

 3      2
x  + 6*x

$$x^{3} + 6 x^{2}$$

d / 3      2\
--\x  + 6*x /
dx

$$\frac{d}{d x} \left(x^{3} + 6 x^{2}\right)$$

Transform

Detail solution

Differentiate $x^{3} + 6 x^{2}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. 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: $12 x$
The result is: $3 x^{2} + 12 x$
Now simplify:

$3 x \left(x + 4\right)$

The answer is:

$3 x \left(x + 4\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2       
3*x  + 12*x

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

Simplify

The second derivative [src]

6*(2 + x)

$$6 \left(x + 2\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of y=x^3+6x^2