Derivatives of Exponential Functions (Edexcel A-Level Mathematics): Quizzes

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Derivatives of Exponential Functions
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What is ddx(ex)\frac{d}{dx}(e^x) equal to?

exe^x

Which base makes an exponential function's derivative equal to itself?

e≈2.718e \approx 2.718

What is ddx(ax)\frac{d}{dx}(a^x) for a general base a>0a > 0?

axln⁡(a)a^x \ln(a)

In ddx(ax)=axln⁡(a)\frac{d}{dx}(a^x) = a^x \ln(a), what role does ln⁡(a)\ln(a) play?

Constant multiplier

What is ddx(eu(x))\frac{d}{dx}(e^{u(x)}) using the chain rule?

eu(x)⋅u′(x)e^{u(x)} \cdot u'(x)

What is ddx(au(x))\frac{d}{dx}(a^{u(x)}) using the chain rule?

au(x)ln⁡(a)⋅u′(x)a^{u(x)} \ln(a) \cdot u'(x)

Find ddx(e3x)\frac{d}{dx}(e^{3x}).

3e3x3e^{3x}

What is ddx(5x)\frac{d}{dx}(5^x)?

5xln⁡(5)5^x \ln(5)

Find ddx(2e−x2)\frac{d}{dx}(2e^{-x^2}).

−4xe−x2-4xe^{-x^2}

Which field uses exponential derivatives to find maxima and minima?

Economics and engineering

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