A function is given by $y = x + \sqrt{x^2 + 2ax + b}$, where $a$ and $b$ are constants. F

Question

A function is given by $y = x + \sqrt{x^2 + 2ax + b}$, where $a$ and $b$ are constants. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$. Find the condition satisfied by $a$ and $b$ such that the gradient function is defined for all $x \in \mathbb{R}$.

Accepted Answer

(i) $\frac{\mathrm dy}{\mathrm dx}=\frac{y+a}{y-x}$, where the radicand is positive. (ii) $b>a^2$.

Techniques of Differentiation - Chain Rule

Techniques of Differentiation - Chain Rule

Solution:

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