Calculus Derivative using Chain Rule Basic

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•
Mathematics
•
10th Grade - University
•
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
Find y' for y = (2x + 1)^{10}.
Back
y' = 20(2x + 1)^{9}.
Tags
CCSS.HSA.APR.C.5
3.
FLASHCARD QUESTION
Front
Find the derivative of f(x) = (x^{3} - 2x)^{2} and simplify.
Back
f'(x) = 6x^{5} - 16x^{3} + 8x.
4.
FLASHCARD QUESTION
Front
Find the derivative of f(x) = 7(3x + 4)^{5}.
Back
f'(x) = 105(3x + 4)^{4}.
5.
FLASHCARD QUESTION
Front
Find the derivative of f(x) = (x^{6} + 4)^{5}.
Back
f'(x) = 30x^{5}(x^{6} + 4)^{4}.
6.
FLASHCARD QUESTION
Front
What is the derivative of a constant?
Back
The derivative of a constant is 0.
7.
FLASHCARD QUESTION
Front
If f(x) = g(h(x)), what is the derivative f'(x) using the Chain Rule?
Back
f'(x) = g'(h(x)) * h'(x).
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