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Question
Find the derivatives of the following functions using first principle.
f(x) = – 4x + 7
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Solution
f(x + Δx) = – 4(x + Δx) + 7
f(x + Δx) – f(x) = [– 4(x + Δx) + 7] – [– 4x + 7]
f(x + Δx) – f(x) = [– 4(x + Δx) + 7] + 4x – 7
f(x + Δx) – f(x) = – 4 Δx
`(f(x + Deltax) - f(x))/(Deltax) = - 4 (Deltax)/(Deltax)`
`lim_(Deltax -> 0) (f(x + Deltax) - f(x))/(Deltax) = lim_(Deltax -> 0) - 4`
`f"'"(x)` = – 4
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