How do you differentiate $- x^{2 + 1}$ $-x^(2+1)$ ?

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Answer 1 · 2017-07-02T02:39:04

$\frac{d}{d x} - x^{2 + 1} = - 3 x^{2}$ $d/(dx) -x^(2+1) = color(blue)(-3x^2$

We're asked to find the derivative of the expression

$- x^{2 + 1}$ $-x^(2+1)$

This can be written as

$\frac{d}{d x} (- x^{3})$ $d/(dx) (-x^3)$

We can first factor out the constant, $- 1$ $-1$ :

$- 1 (\frac{d}{d x} x^{3})$ $-1(d/(dx) x^3)$

Using the power rule:

$\frac{d}{d x} x^{n} = n x^{n - 1}$ $d/(dx) x^n = nx^(n-1)$

$\frac{d}{d x} x^{3} = 3 x^{3 - 1} = 3 x^{2}$ $d/(dx) x^3 = 3x^(3-1) = 3x^2$

Lastly, multiplying by $- 1$ $-1$ gives

$\frac{d}{d x} - x^{3} = - 3 x^{2}$ $d/(dx) -x^3 = color(blue)(-3x^2$

How do you differentiate −x2+1-x^(2+1)?