Find the derivative of (5x^{3} + 3x - 1)(x - | vedclass

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Question

(A) Let $f(x) = (5x^{3} + 3x - 1)(x - 1)$.Using the product rule,$\frac{d}{dx}[u(x)v(x)] = u(x)v'(x) + v(x)u'(x)$:$f'(x) = (5x^{3} + 3x - 1)\frac{d}{d

Vedclass · Accepted Answer

$20x^{3} - 15x^{2} + 6x - 4$

Vedclass · Answer

(A) Let $f(x) = (5x^{3} + 3x - 1)(x - 1)$.Using the product rule,$\frac{d}{dx}[u(x)v(x)] = u(x)v'(x) + v(x)u'(x)$:$f'(x) = (5x^{3} + 3x - 1)\frac{d}{dx}(x - 1) + (x - 1)\frac{d}{dx}(5x^{3} + 3x - 1)$$f'(x) = (5x^{3} + 3x - 1)(1) + (x - 1)(15x^{2} + 3)$$f'(x) = 5x^{3} + 3x - 1 + (15x^{3} + 3x - 15x^{2} - 3)$$f'(x) = 5x^{3} + 15x^{3} - 15x^{2} + 3x + 3x - 1 - 3$$f'(x) = 20x^{3} - 15x^{2} + 6x - 4$.

Find the derivative of $(5x^{3} + 3x - 1)(x - 1)$.

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