A spruce tree is approximately the shape of a cone with a slant height of 20 ft. The angle formed by the tree with the ground me
asures 72 degrees. Estimate the height of the tree. Round to the nearest foot.
(picture below)
(picture below)
2 answers:
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Use the power, product, and chain rules:
• product rule
• power rule for the first term, and power/chain rules for the second term:
• power rule
Now simplify.
You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.
On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify
Differentiate both sides and you end up with the same derivative:
