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The derivative of the function/ y=x³/x²+1

You entered:

y=x³/x²+1

What you mean?

x^3/(x^2) + 1

x^((3/x)^2) + 1

x^3/(x^2 + 1)

x^3/(x^2) + 1

x^3*2/x + 1

x^3/(x^2) + 1

x^3*2/x + 1

Derivative of y=x³/x²+1

The solution

You have entered [src]

$$\frac{x^{3}}{x^{2}} + 1$$

  / 3    \
d |x     |
--|-- + 1|
dx| 2    |
  \x     /

$$\frac{d}{d x} \left(\frac{x^{3}}{x^{2}} + 1\right)$$

Transform

Detail solution

Differentiate $\frac{x^{3}}{x^{2}} + 1$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x^{3}$ and $g{\left(x \right)} = x^{2}$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  Now plug in to the quotient rule:
  
  $1$
2. The derivative of the constant $1$ is zero.
The result is: $1$

The answer is:

$1$

The first derivative [src]

$$\frac{3 x^{2}}{x^{2}} - 2$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify