Q.State whether the following statement is true or false:
If $y = 20 + 15x + x^2$ then $\frac{dx}{dy} = \frac{1}{15 + 2x}$

$\dfrac{dy}{dx}=15+2x$, and $\dfrac{dx}{dy}=\dfrac{1}{dy/dx}=\dfrac{1}{15+2x}$, so the statement is True.

Differentiate $y = 20 + 15x + x^2$ with respect to $x$:

$\frac{dy}{dx} = 0 + 15 + 2x = 15 + 2x.$

By the inverse-function relationship (valid where $\tfrac{dy}{dx}\neq 0$):

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