What is the derivative of the function f(x) = $$a^x$$ where a is a constant?

f'(x) = $$a^x \times \frac{ln(a)}{dx}$$ .

Find the derivative of f(x) = $$\frac{x^2}{e^x}$$ .

f'(x) = $$\frac{(2x e^x - x^2 e^x)}{(e^x)^2}$$ .

Find the derivative of f(x) = $$-8x^{-3} + 5x - e^x$$ .

f'(x) = $$24x^{-4} + 5 - e^x$$ .

Find the derivative of f(x) = $$\frac{1}{e^x}$$ .

f'(x) = $$-\frac{e^x}{(e^x)^2} = -\frac{1}{e^x}$$ .

What is the derivative of $$\frac{a^x}{b^x}$$ ?

f'(x) = $$\frac{a^x \times ln(a) - b^x \times ln(b)}{(b^x)^2}$$ .

Derivatives of Exponential Function Flashcards

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4.

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What is the product rule for derivatives?

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If u and v are functions of x, then the derivative of their product is: (uv)' = u'v + uv'.

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6.

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What is the chain rule for derivatives?

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If y = f(g(x)), then the derivative is: dy/dx = f'(g(x)) * g'(x).

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