Calculus Chapter 3 Review

Chain Rule

100

What is the derivative of f(g(x))?

f'(g(x))g'(x)

200

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300

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400

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Implicit Differentiation

100

Implicitly differentiate y=x

dy/dx = 1

200

What is the Derivative of  y⁴+y³+y²=x²

dy/dx = 2x/(4y³+3y²+2y)

300

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400

Find the points of the function in which the slope is Horizontal.

3y²+x=x²

(0,0) x=0 y=0

Natural Log and Exponential Differentiation

100

What is the derivative of e^x

e^x

200

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300

What is the derivative of log₄(x)

1/(xln4)

400

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Inverse Differentiation

100

If f(x) and g(x) are inverses, and f(4)=3 then what do we know about g(x)

g(3)=4

200

What is the derivative of arctan(x)?

1/(1+x²)

300

If g(x)=x²+4x and f(x) are inverses of each other, and the derivative of g(2)=10 what is f'(10)

f'(10)=1/8

400

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