BC Calculus Test 2 Derivative rules and Rectalinear motion Questions and Answers
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BC Calculus Test 2 Derivative rules and Rectalinear motion Questions and Answers
Derivative Notation
D(x)f(x) means the derivative wrt x
With the big bar it means to evaluate at a specific value
Second derivative is derivative of derivative
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BC Calculus Test 2 Derivative rules and
Rectalinear motion Questions and
Answers
Higher order derivatives - answer
Derivative Notation - answer D(x)f(x) means the derivative wrt x
With the big bar it means to evaluate at a specific value
Second derivative is derivative of derivative
Derivative Rules - answer
Power rule proof for negative integers - answer look at f(x) = x^(-n) as 1/x^n, then
use the quotient rule
Prove the derivative of a constant - answer Start out with limit definition, then when
subtracting you know something is a real zero vs approaching zero
Prove sum rule - answer
Prove derivative times constant - answer
Derivatives of trig functions - answer Tangent: Split into sine and cosine, then
product
cotangent: Same as tangent to split
Secant: Split into 1/cosine
Other way for cotangent is to split into 1/tan
Can also do def. of derivative with tangent and then use an identity and multiply by
jonjugate
Related Rates - answer Question will specify some specific rate and so then you do
the dy/dx for the specific variables, then based on the problem, you will be able to use
other equations to find the answer
Chain rule - answer When doing the chain rule, when you have that second function,
take the value of that funtion and plug it into the derivative at the next,
If you have two functions and one of the variables in the primary function can be related
with another, you can do the chain rule of dA/dr * dr/dt and multiply by the derivative of
the secondary function to get the relation of the first and the other variable.
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