FLASHCARD - Chain Rule and Implicit Differentiation

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Chain Rule in calculus?
Back
The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).
2.
FLASHCARD QUESTION
Front
Differentiate y = sin(2x^2).
Back
y' = 4x cos(2x^2).
3.
FLASHCARD QUESTION
Front
What is Implicit Differentiation?
Back
Implicit Differentiation is a technique used to differentiate equations that define y implicitly in terms of x, rather than explicitly as y = f(x).
4.
FLASHCARD QUESTION
Front
Find dy/dx for the equation 9y + x = 4y.
Back
dy/dx = -1/5.
5.
FLASHCARD QUESTION
Front
Differentiate y = e^(5x) + 1.
Back
y' = 5e^(5x).
6.
FLASHCARD QUESTION
Front
What is the product rule in differentiation?
Back
The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is given by (uv)' = u'v + uv'.
7.
FLASHCARD QUESTION
Front
Differentiate f(x) = x^7 (5 + 8x)^3.
Back
f '(x) = x^6 (5 + 8x)^2 (35 + 80x).
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