题目 Implicit differentiation can be useful when functions involve trigonometric expressions, exponentials, or logs. Find the derivative of y with respect to x for each of the following.sin (x+y)+cos (x-y)=1 相关知识点: 试题来源: 解析 sin (x+y)+cos (x-y)=1 反馈 收藏 ...
Implicit Differentiation: Differentiation is the rate of change of one variable in relation to another. Implicit functions are those functions that are not given in the form y=f(x) but given in a more complicated form in which it is...
Differentiation in calculus: The given equation is consisting of three variables x,y,z and we need to find out dz dt so we'll apply implicit differentiation with respect to t and use the derivative power rule d dx(xn)=nxn−1 . Next we'll take al...
To find dydx for the equation xsin(2y)=ycos(2x), we will use implicit differentiation and the product rule. Here’s a step-by-step solution: Step 1: Differentiate both sides with respect to xStarting with the equation:xsin(2y)=ycos(2x)We differentiate both sides with respect to x. St...
Learn about implicit differentiation and understand how to find the derivative of y. Explore the implicit differentiation formula with examples of how it's used. Related to this Question xy = x^2 - y^2 Find \frac{dy}{dx}. Find \frac{d}{dx} (\frac{x^2+1}{x+1}) ...
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Derivative = rate of change When we say “rate of change” without specifying what it's with respect to, we mean “rate of change with respect to time”. –example: velocity- change in distance with respect to time If the variable is different from time use implicit differentiation Unless ...
Logarithmic Differentiation: In order to differentiate a complicated function like {eq}y = (f(x))^(g(x)), {/eq} we use logarithmic differentiation. First we take the natural log of both sides: {eq}\begin{eqnarray*}\ln y & =& \ln (f(x))^(g(x)) \\ & = & g(x) \ln ...
Use implicit differentiation to find partial z/partial x and partial z/partial y. x^2 + 2y^2 + 3z^2 = 2. Find the general solution for the differential equation. y'=(x+1)^2 Find an integrating factor for the following differential equation: (y ...