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The derivative $$f'(x_0)$$ gives the slope of the tangent to the curve $$y = f(x)$$ at point $$(x_0, y_0)$$.
$$m_{\mathrm{tangent}} = \left. \frac{dy}{dx} \right|_{(x_0,y_0)} = f'(x_0)$$
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The derivative $$f'(x_0)$$ gives the slope of the tangent to the curve $$y = f(x)$$ at point $$(x_0, y_0)$$.
$$m_{\mathrm{tangent}} = \left. \frac{dy}{dx} \right|_{(x_0,y_0)} = f'(x_0)$$
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