Implicit Differentiation
Read this topicExplanations 7
- Here's an example: Find the slope of the line tangent to the circle x2+y2=25x^2+y^2=25x2+y2=25 at point (3,4)(3,4)(3,4). We know we can do it geometrically... But not now. We wa…
By Yuan Yao, Alex Federspiel
- Implicit Differentiation The Chain Rule States: dydx=dydududx\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}dxdy=dudydxdu Or f(x)=g(h(x)) ⟹ f′(x)=g′(x)h′(g(x))f(x)= g(h(x)) \implies…
By Yan Yau Cheng, Alex Federspiel
- Implicit Functions In algebra or calculus, we call an equation implicit if it is of the form R(x1,⋯ ,xn)=0\mathcal{R}\left(x_1,\cdots,x_n\right)=0R(x1,⋯,xn)=0, where R\mathcal…
By Ahaan Rungta, Moor Xu
- (Videos) An Introduction to Implicit Differentiation by PatrickJMT Here's a video by patrickJMT explaining what an implicit equation is and how you go about solving it. Before w…
By Alex Federspiel
- (Videos) Implicit Differentiation Examples by PatrickJMT Here's a video by patrickJMT going over some basic examples of implicit differentiation and working through the examples…
By Alex Federspiel
- (Videos) Compilation of Implicit Differentiation Examples by PatrickJMT Here's a video by patrickJMT where he goes over some implicit differentiation examples. Implicit differen…
By Alex Federspiel
- (Video) Deriving the Derivative of Inverse Tangent by PatrickJMT Here's a good video by patrickJMT showing you how to derive the derivative of inverse tangent. This is helpful b…
By Alex Federspiel
Problems 12
- What is the tangent line to (x2+y2)3=8x2y2(x^2 + y^2)^3 = 8x^2y^2(x2+y2)3=8x2y2 at the point (−1,1)(-1,1)(−1,1)?
- The curve y2=x3+1y^2 = x^3 + 1y2=x3+1 is tangent, at the point (x0,y0)(x_0,y_0)(x0,y0), to a circle centered at (4,0)(4,0)(4,0). Find the sum of all possible values of 99x099x…
- Find dydx\frac{dy}{dx}dxdy of x3y3−y=xx^3y^3-y=xx3y3−y=x
- Let y=xxy = x^xy=xx for x>0x > 0x>0. What is dydx\frac{dy}{dx}dxdy?
- Find dydx\dfrac{dy}{dx}dxdy for xsiny=ysinxx\sin y=y\sin xxsiny=ysinx.
- Find dydx\frac{dy}{dx}dxdy for y4+x3y2=6+x6yy^4+x^3y^2=6+x^6yy4+x3y2=6+x6y
- Find dydx\frac{dy}{dx}dxdy for tan(xy)=x2+3y2\tan\bigg(\frac xy\bigg)=x^2+3y^2tan(yx)=x2+3y2
- Find dydx\frac{dy}{dx}dxdy for eylnx=2y\sqrt{e^y\ln x}=2^yeylnx=2y
- Find an equation of a line tangent to the curve x2+4xy−2y2+x=6x^2+4xy-2y^2+x=6x2+4xy−2y2+x=6 at the point (2,4)(2,4)(2,4).
- Find yyy'' x+y=1\sqrt x+\sqrt y=1x+y=1
- Find the derivative. arctan(xy)=1+xy\arctan(xy)=1+xyarctan(xy)=1+xy
- Consider this function which models an arc with endpoints at (±1,0):(\pm 1, 0):(±1,0): y=231−x2.y = \frac{2}{3}\sqrt{1 - x^2}.y=321−x2. Convert this function to polar coordina…