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Question
Find the derivative of x–3 (5 + 3x).
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Solution
Let f (x) = x– 3 (5 + 3x) ...(1)
Differentiating (1) with respect to x, we get
f'(x) = (x-3) (5 + 3x) + (x-3) (5 + 3x)
= f'(x) = (-3) x-3-1 (5 + 3x) + (x-3) (0 + 3)
= `3x-4 (5 + 3x) + x-3. (3)
= -15x-4 + 9x-3 + 3x-3
= -15x-4 - 6x-3
= `(-15)/x^4 - 6/x^3`
∴ f'(x) = `(-3)/ x^4 (5 + 2x)`
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