Find the derivative of each of the following with respect to $x$. \(y = -5x^{-2} + \frac{1}{3}x^6

Question

Find the derivative of each of the following with respect to $x$. $y = -5x^{-2} + \frac{1}{3}x^6 + 1$ $y = \frac{5}{2x^2} - \frac{3\sqrt{x}}{5} + 18\sqrt[9]{x}$ $y = \frac{-3x^5 + 6x^4 - 2x^2 + 4}{x^2}$ $y = \frac{x^3 + 2x^2 - x + 1}{\sqrt{x}}$

Accepted Answer

(i) $\dfrac{10}{x^3}+2x^5$ (ii) $-\dfrac{5}{x^3}-\dfrac{3}{10\sqrt{x}}+\dfrac{2}{\sqrt[9]{x^8}}$ (iii) $-9x^2+12x-\dfrac{8}{x^3}$ (iv) $\dfrac52\sqrt{x^3}+3\sqrt{x}-\dfrac{1}{2\sqrt{x}}-\dfrac{1}{2\sqrt{x^3}}$

Differentiation - Power Rule and Derivatives of Algebraic Functions

Differentiation - Power Rule and Derivatives of Algebraic Functions

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