Basic Mathematics20785 marksNumerical: implicit differentiation, slopeImplicit differentiation
Find fracdydx if y2 - x2 = sin x. Find the slope of circle x2 + y2 = 25 at the point (3,4). [2.5+2.5]
Find $\frac{dy}{dx}$ if $y^2 - x^2 = \sin x$. Find the slope of circle $x^2 + y^2 = 25$ at the point $(3,4)$. [2.5+2.5]
- Part 1: $y^2 - x^2 = \sin x$ - Part 2: Circle $x^2 + y^2 = 25$, point $(3, 4)$ --- (a) Find $\frac{dy}{dx}$ if $y^2 - x^2 = \sin x$ Differentiate both sides with respect to $x$: $$\frac{d}{dx}(y^2 - x^2) = \frac{d}{dx}(\sin x)$$ $$2y\frac{dy}{dx} - 2x = \cos x$$ Isolate $\frac{dy}{dx}$: $$2y\fr...