Question on: SS3 Mathematics - Differential Calculus (Differentiation)
Find the differential coefficient of \(y = x^{5} + 4x^{3} - 5x + 4\)
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A
\(5x^{4} + 12x^{2} - 5\)
B
\(\5x^{4} + 12x^{2} - 5x\)
C
\(\5x^{4} + 6x^{2} - 5\)
D
\(\x^{4} + 12x^{2} - 5\)
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Correct Option: A
\[y = x^{5} + 4x^{3} - 5x + 4\]
\[\frac{dy}{dx} = \frac{d}{dx}(x^{5} + 4x^{3} - 5x + 4)\]
\[\frac{dy}{dx} = \frac{d}{dx}\left( x^{5} \right) + \frac{d}{dx}\left( 4x^{3} \right) - \frac{d}{dx}(5x) + \frac{d}{dx}(4)\]
\(\frac{dy}{dx} = 5x^{4} + 12x^{2} - 5 + 0 = 5x^{4} + 12x^{2} - 5\)
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