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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In Problems 11-20, find the directional derivative of the given function at the given point in the indicated direction. 11. f (x,y)= 5x3y6;(−1,1),θ= π/6 12. f (x,y)= 4x+xy2 −5y;(3,−1),θ =π/4 13. f

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

Transcribed image text: Find the numerical derivative of the given function at the indicated point. Use h = 0.001. Use h = 0.001. Is the function differentiable at the indicated point? f(x)= 4x

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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