How do you differentiate #x^pi-pix#?
Let's differentiate the expression using the "power rule":
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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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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.
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.
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.
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.
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