WebAnswer (1 of 3): Hope you can understand the handwriting:) Webx x (1 + log ⁡ x) Finding the value of dy dx: The given function is y = x x. Taking log on both sides, log y = x log x. Differentiating with respect to x. 1 y dy dx = log x + x × 1 x [∵ d dx log x = 1 x, d (a · b) dx = a db dx + b da dx] = 1 + logx dy dx = y [1 + logx] = x x [1 + logx] Hence, the correct option is C.

Solve dy/dx=dy/x(y-x) Microsoft Math Solver

WebDifferential equations of the form \frac {dy} {dx}=f (x) dxdy = f (x) are very common and easy to solve. The following shows how to do it: Step 1 First we multiply both sides by dx dx to obtain dy=f (x)~dx. dy = f (x) dx. Step 2 Then we take the integral of both sides to obtain WebIf x x+x y+y x=a b, then find dxdy. Hard Solution Verified by Toppr Given, x x+x y+y x=a b Let p=x x,q=x y,r=y x Let us take p=x x Take log on both sides logp=xlogx ⇒ … lady tub pancake

If xx = yy then (dy /dx) is - Tardigrade

WebIf x y - y x = a b, find d y d x. Advertisement Remove all ads Solution The given function is x y - y x = a b Let x y = u and y x = v Then , the function becomes u - v = a b u x v x d u d x - d v d x = 0 ..... (1) u = x y ⇒ log u = log (x y) ⇒ log u = y log x Differentiating both sides with respect to x, we obtain WebMulitply both sides by d x d ( x y) = y x y − 1 d x + x y ln ( x) d y, d ( y x) = y x ln ( y) d x + x y x − 1 d y As you can see, the derivative is of x y and y x is the derivative with respect to x on the left side + the derivative with repsect to y on the right side. So, d y d x ( x y ln ( x) … WebImplicit differentiation helps us find dy/dx even for relationships like that. This is done using the chain rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of y² would be 2y⋅ (dy/dx). Created by Sal Khan. Sort by: Top Voted Questions Tips & Thanks Jack 10 years ago jed 2300