# 1.6 Derivatives

**The use of calculators or other technologies are strictly prohibited for this assignment.**

## 1 Understanding Derivatives as Slopes

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a) The slope of a straight line doesn't change for any $x$. What's the derivative (slope) of the function $f(x) = 2 x + 3$?

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b) What's the derivative (slope) of the function $f(x) = 0.5 x + 4$?

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## 2 Derivative of a Constant; Power Rule; Sums Rule

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a) Find the derivative of $f(x) = x^0$.

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b) Find the derivative of $f(x) = 2$.

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c) Find the derivative of $f(x) = 3 x^2$.

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d) Find the derivative of $f(x) = 4 x^3$.

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e) Find the derivative of $f(x) = 4 x^3 + 3 x^2$.

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f) Find the derivative of $f(x) = 4 x^3 + 3$.

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## 3 Derivative of the Natural Log

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Find the derivatives of:

a) Find the derivative of $f(x) = \ln(x)$.

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b) What is the derivative of $f(x) = \ln(x)$ evaluated at $x = 4$?

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c) Find the derivative of $f(x) = 3\ln(x)$.

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