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Question
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`a/x^4 = b/x^2 + cos x`
Solution
Let f(x) = `a/x^4 - b/x^2 + cos x`
= `d/dx (a/x^4) - d/dx (b/x^2) + d/dx (cos x)`
= `a d/dx (x^(-4)) - b d/dx (x^(-2)) + d/dx (cos x)`
= `a (-4x^(-5)) - b(-2 x^-3) + (-sin x)` `[d/dx (x^n) = nx^(n - 1) and d/dx (cos x) = -sin x]`
= `(-4a)/x^5 + (2b)/x^3 - sin x`
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