Log/Exponential Functions (Leaving Cert Mathematics): Quizzes

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Log/Exponential Functions
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What defines an exponential function?

Variable appears in the exponent

What is ln⁡(x)\ln(x) the inverse of?

Exponential function with base ee

What is ddxln⁡(x)\frac{d}{dx} \ln(x)?

1x\frac{1}{x}

What is ddxex\frac{d}{dx} e^x?

exe^x

What is ddxeax\frac{d}{dx} e^{ax} where aa is a constant?

aeaxa e^{ax}

What is ddxax\frac{d}{dx} a^x where aa is a constant?

axln⁡(a)a^x \ln(a)

What rule is often needed for complex exponential and logarithmic expressions?

Chain rule

If f(x)=eg(x)f(x) = e^{g(x)}, what is f′(x)f'(x)?

eg(x)×g′(x)e^{g(x)} \times g'(x)

When is logarithmic differentiation particularly useful?

Products, quotients, variable bases

What is ddxesin⁡(x)\frac{d}{dx} e^{\sin(x)}?

cos⁡(x)esin⁡(x)\cos(x) e^{\sin(x)}

Explore Leaving Cert Mathematics Revision Notes by Topics

Product Rule & Quotient Rule

Chain Rule

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Product Rule & Quotient Rule

Chain Rule

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Product Rule & Quotient Rule

Chain Rule

Explore Leaving Cert Mathematics Exam Questions by Topics

Product Rule & Quotient Rule

Chain Rule

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