find dy/dx using differentiation if y= 7^y - 10/ x^2 +4x
Added by Sabrina G.
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However, since \(y\) is a function of \(x\), we will use implicit differentiation. Show more…
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Find dy/dx in terms of x and y if x ln y + y^7 = 4 ln x.
Suman Saurav T.
To find dy/dx = y' for x^7 + y^4 = 5, we differentiate both sides of the equation with respect to x. On the right-hand side, we have the following. d/dx[5] = 0 On the left-hand side, we have d/dx[x^7 + y^4]. We already know that d/dx[y^4] = 4y^3y'. For the term x^7, we have the following. d/dx[x^7] = 7x^6 Step 3 We now have d/dx[x^7 + y^4] = 7x^6 + 4y^3y' = d/dx[5] = 0. Rearranging this, we get the following. 4y^3y' = Solving for y', we conclude that the derivative dy/dx is as follows. dy/dx =
Adi S.
Find $d y / d x$ by implicit differentiation. $$4 x y+\ln x^{2} y=7$$
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