WebIf x 2 + y 2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is – 34.. Explanation: Given, x 2 + y 2 + sin y = 4. After differentiating the ... WebThe derivative so gives the slope of a tangent line that touches a curve only once. The slope formula in contrast gives the slope of a secant ( a line that intersects a curve twice) through a curve as it uses two points with significant difference. The small delta symbol (δ) is also sometimes used to show a very very small change. 4 comments
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WebJun 10, 2024 · What is the antiderivative of x x2 + 4? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Andrea S. Jun 10, 2024 ∫ xdx x2 +4 = 1 2 ln(x2 +4) +C Explanation: Substitute t = x2 +4, dt = 2xdx, so that: ∫ xdx x2 +4 = 1 2 ∫ dt t = 1 2ln t +C and undoing the substitution: ∫ xdx x2 +4 = 1 2 ln(x2 +4) +C Answer link WebAug 29, 2016 · What is the derivative of √4 − x2? Calculus Basic Differentiation Rules Chain Rule 1 Answer Jim G. Aug 29, 2016 −x √4 −x2 Explanation: Differentiate using a combination of power and chain rule Reminder of chain rule ∣∣ ∣ ∣ ∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a a dy dx = dy du × du dx a a ∣∣ ∣ … how does oxygen help shortness of breath
Worked example: Implicit differentiation (video) Khan Academy
WebTranscribed Image Text: Use the derivative to find the vertex of the parabola. y=-x² - 4x + 4 Let f(x) = y. Find the derivative of f(x). f'(x) = The vertex is (Type an ordered pair.) Expert Solution. Want to see the full answer? Check out a sample Q&A here. ... Identify which step is incorrect in graphing g(x) = -2(x-1)4-1 Step 1: ... WebNov 20, 2011 · Cheap, non-rigorous, non-mathematical, engineering-type answer: sgn(x) ("signum x", the sign of x, being -1 for x<0 and +1 for x>0).Note that sgn(0) = 0, which is a practical compromise, being the average of -1 ("coming from the negatives") and +1 ("coming from the positives").. Of course we all know that d x /dx is not defined at … WebTherefore, to find the directional derivative of f (x, y) = 8 x 2 + y 3 16 at the point P = (3, 4) in the direction pointing to the origin, we need to compute the gradient at (3, 4) and then … how does oxygen move into a cell