Differentiation rules and techniques: pick a function and decide first whether it needs the product, quotient or chain rule. Once you name the right rule, the working and the pieces of the gradient appear, and you can move a point along the curve to see the rule build the gradient of the tangent
Name the rule first, and the working follows
The algebra is the easy part once you know which rule you need. So decide first: is the whole thing a product, a quotient or a function inside a function? Pick a function and name its rule. The working only opens once you get it right; then move the point and watch the pieces of the gradient change.
Build the gradientgradient 3.25
Pick a function. Name its rule first. Then move the point.
The function h(x)
Which rule does it need?
Point on the curvex = 0.5
Gradient by the rule
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h′(x) from the pieces
Tiny chord check
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slope from x − 0.001 to x + 0.001
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Know this
A product needs u′v + uv′, a quotient needs (vu′ − uv′)/v², and a function inside a function needs the chain rule, so read the outermost operation first and work inwards.