If $y=x$ and $z=\dfrac{1}{x}$, then $\dfrac{dy}{dz} =$ (a) $-x^{2}$ (b) $x^{2}$ (c) $-\dfrac{1}{x^{2}}$ (d) $1$

If y=x and z=(1)/(x), then (dy)/(dz) = (a) -x² (b) x² (c) -dfrac1x² (d) 1

Question 29 of 49

y=x

(a)

-x^{2}

(b)

x^{2}

(c)

-\dfrac{1}{x^{2}}

(d)

1

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2022MCQ· 1mImportance★★★★★

59% · 29/49 Questions

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Differentiate both with respect to $x$ and use $\tfrac{dy}{dz}=\tfrac{dy/dx}{dz/dx}=\tfrac{1}{-1/x^2}=-x^2$ .

Both $y$ and $z$ are given as functions of $x$ , so use the chain-rule ratio $\dfrac{dy}{dz}=\dfrac{dy/dx}{dz/dx}$ .

$y = x \;\Rightarrow\; \frac{dy}{dx} = 1$ …