In this video I cover how to find the derivative of a function at a single point. This is done by using limits and the difference quotient. Remember that w
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We define the derivative of f with respect to x evaluated at x = a, denoted f ′ (a), by the formula f ′ (a) = lim h → 0f(a + h) − f(a) h, provided this limit exists. Aloud, we read the
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f ′ ( x) | x = 0 = lim h → 0 f ( 0 + h) − f ( 0) ( 0 + h) − 0. = lim h → 0 h 2 cos h − 0 h. = lim h → 0 ( h cos h) = ( lim h → 0 h) ⋅ ( lim h → 0 cos h) = 0 × 1 = 0. This is totally as per the
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