L17 - L17 – Implicit Differentiation Explicit Equations...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L17 – Implicit Differentiation Explicit Equations Implicit Equations Assume y is a differentiable function of x 1) Differentiate with respect to x on both sides of the equation. dy terms on one side dx dy dx 2) Collect all 3) Factor out 4) Solve for dy dx 1 d x dx d2 x dx d y dx d2 y dx Find dy if x2 + y 2 = 9 . dx a) Implicitly 2 b) Explicitly c) Show that they are the same. 3 Find the horizontal and vertical tangent lines to x2 − 2x + y 2 + 6y = 15 . 4 Find the slope of the tangent line to 2x2 − xy = x + 4 at ( 1, −1 ) . y3 5 Find dy if y = tan(xy ) . dx Two curves are called orthogonal if at each point of intersection, their tangent lines are perpendicular. Two families of curves are orthogonal trajectories if every curve in one family is orthogonal to every curve in the other. 6 Show that the hyperbolas xy = c for c = 0 are orthogonal trajectories to the hyperbolas x2 − y 2 = k for k = 0 . 7 Find d sin−1 (x) dx 8 If f (x) = sin−1 (2x − 1), find the derivative, the domain of f (x) and the domain of its derivative. d cos−1 (x) = dx 9 Find the derivative of y = tan−1 (x) . Find the derivative of f (x) = tan−1 ( x − √ 1 + x2 ) . 10 d csc−1 (x) = dx d sec−1 (x) = dx d cot−1 (x) = dx 11 If g (x) = x tan−1 (x), find g (x) . 12 ...
View Full Document

Page1 / 12

L17 - L17 – Implicit Differentiation Explicit Equations...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online