Differentiation Rules

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if f(x) = gh(x), give f’(x).

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1

if f(x) = gh(x), give f’(x).

f’(x) = g’h(x) x h’(x)

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2

if f(x) = g(x) x h(x), give f’(x).

f’(x) = g(x) x h’(x) + h(x) x g’(x)

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3

if f(x) = ln x, give f’(x).

f’(x) = 1 / x

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4

if f(x) = e^x, give f’(x).

f’(x) = f(x) = e^x

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5

if f(x) = a^x, give f’(x), showing how you got that result.

f(x) = a^x = e^(xln a).

∴ f’(x) = ln a x e^(xln a) = ln a x a^x

∴ f’(x) = ln a x a^x

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