Question

Find the first derivative of the following: (i) $y = 12x^3 - 8x^2 + 7x + 5$ (ii) $y = 5x^4 - 8x^2 + \frac{x^2}{5} + 3$ (iii) $f(x) = 8\sqrt{x} - 6x^3$ (iv) $g(x) = 5x \cos(2x^3)$ (v) $y = \sin(3x^2) + \cos(x)$ (vi) $h(t) = \frac{5t + 6}{\sqrt{t}}$

          Find the first derivative of the following:
(i) $y = 12x^3 - 8x^2 + 7x + 5$
(ii) $y = 5x^4 - 8x^2 + \frac{x^2}{5} + 3$
(iii) $f(x) = 8\sqrt{x} - 6x^3$
(iv) $g(x) = 5x \cos(2x^3)$
(v) $y = \sin(3x^2) + \cos(x)$
(vi) $h(t) = \frac{5t + 6}{\sqrt{t}}$

Find the first derivative of the following:
(i) y = 12x^3 - 8x^2 + 7x + 5
(ii) y = 5x^4 - 8x^2 + (x^2)/(5) + 3
(iii) f(x) = 8√(x) - 6x^3
(iv) g(x) = 5x cos(2x^3)
(v) y = sin(3x^2) + cos(x)
(vi) h(t) = (5t + 6)/(√(t))

Added by Ashley M.

Calculus: Early Transcendentals

James Stewart 8th Edition

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10/18/2023

Step 1

Step 1: (i) $\frac{dy}{dx} = \frac{d}{dx}(12x^3 - 8x^2 + 7x + 5) = 36x^2 - 16x + 7$ (ii) $\frac{dy}{dx} = \frac{d}{dx}(5x^4 - 8x^2 + \frac{x^2}{5} + 3) = 20x^3 - 16x + \frac{2x}{5}$ Show more…

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Find the first derivative of the following: (i) $y = 12x^3 - 8x^2 + 7x + 5$ (ii) $y = 5x^4 - 8x^2 + \frac{x^2}{5} + 3$ (iii) $f(x) = 8\sqrt{x} - 6x^{\frac{1}{3}}$ (iv) $g(x) = 5x \cos(2x^3)$ (v) $y = \sin(3x^2) + \cos(x)$ (vi) $h(t) = \frac{5t + 6}{\sqrt{t}}$

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Find the first derivative of the following: (i) $y = 12x^3 - 8x^2 + 7x + 5$ (ii) $y = 5x^4 - 8x^2 + \frac{x^2}{5} + 3$ (iii) $f(x) = 8\sqrt{x} - 6x^3$ (iv) $g(x) = 5x \cos(2x^3)$ (v) $y = \sin(3x^2) + \cos(x)$ (vi) $h(t) = \frac{5t + 6}{\sqrt{t}}$

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