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How do you differentiate #x^pi-pix#?

Answer 1

Luke Alvarez

#pi (x^(pi - 1) - 1)#

We have: #x^(pi) - pi x#

Let's differentiate the expression using the "power rule":

#=> (d) / (dx) (x^(pi) - pi x) = pi cdot (x)^(pi - 1) - pi#

#therefore (d) / (dx) (x^(pi) - pi x) = pi (x^(pi - 1) - 1)#

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Answer 2

Charles Anctil

To differentiate ( x^{\pi} - \pi x ), you would apply the power rule and the constant multiple rule of differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ).

Differentiating ( x^{\pi} ) with respect to ( x ) using the power rule, we get:

[ \frac{d}{dx}(x^{\pi}) = \pi x^{\pi - 1} ]

Differentiating ( - \pi x ) with respect to ( x ) using the constant multiple rule, we get:

[ \frac{d}{dx}(-\pi x) = -\pi ]

Therefore, the derivative of ( x^{\pi} - \pi x ) with respect to ( x ) is:

[ \pi x^{\pi - 1} - \pi ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.