Log Derivative Quick Check Worksheet
Calculus Warm-Up
Logarithm Properties
Name:
Date:
Pd:
Apply properties of logarithms to expand, condense, simplify, or solve each expression below.
1. Expand Completely Product / Quotient / Power
\(\ln\left(\frac{x^4 \sqrt{y}}{z^3}\right)\)
Ans:
2. Condense to Single Log Single Argument
\(3\ln(x) + \frac{1}{2}\ln(x^2 + 1) - \ln(2x - 3)\)
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3. Simplify Using Inverses Natural Base \(e\)
\(e^{\ln(5x^3)} - \ln\left(e^{2x}\right) + \ln(1)\)
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4. Solve for \(x\) Domain: \(x > 0\)
\(\ln(x) + \ln(x - 2) = \ln(8)\)
Ans:
Front Side • Turn over for Implicit Differentiation
Cut here for 2 half-page copies
Calculus Warm-Up
Logarithm Properties
Name:
Date:
Pd:
Apply properties of logarithms to expand, condense, simplify, or solve each expression below.
1. Expand Completely Product / Quotient / Power
\(\ln\left(\frac{x^4 \sqrt{y}}{z^3}\right)\)
Ans:
2. Condense to Single Log Single Argument
\(3\ln(x) + \frac{1}{2}\ln(x^2 + 1) - \ln(2x - 3)\)
Ans:
3. Simplify Using Inverses Natural Base \(e\)
\(e^{\ln(5x^3)} - \ln\left(e^{2x}\right) + \ln(1)\)
Ans:
4. Solve for \(x\) Domain: \(x > 0\)
\(\ln(x) + \ln(x - 2) = \ln(8)\)
Ans:
Front Side • Turn over for Implicit Differentiation
Calculus Practice
Implicit Differentiation
Find \(\frac{dy}{dx}\) • Back Side
Differentiate implicitly with respect to \(x\). Clearly show all derivative steps, collect \(\frac{dy}{dx}\) terms, and isolate \(\frac{dy}{dx}\).
Problem 1 Find \(\frac{dy}{dx}\)
\[x^2 + 3xy + y^2 = 10\]
Show work below:
\(\frac{dy}{dx} =\)
Problem 2 Contains \(\ln(y)\)
\[x^2 + \ln(y) = 3xy\]
Show work below:
\(\frac{dy}{dx} =\)
Back Side • Simplify final fractions completely
Cut here for 2 half-page copies
Calculus Practice
Implicit Differentiation
Find \(\frac{dy}{dx}\) • Back Side
Differentiate implicitly with respect to \(x\). Clearly show all derivative steps, collect \(\frac{dy}{dx}\) terms, and isolate \(\frac{dy}{dx}\).
Problem 1 Find \(\frac{dy}{dx}\)
\[x^2 + 3xy + y^2 = 10\]
Show work below:
\(\frac{dy}{dx} =\)
Problem 2 Contains \(\ln(y)\)
\[x^2 + \ln(y) = 3xy\]
Show work below:
\(\frac{dy}{dx} =\)
Back Side • Simplify final fractions completely
