To find dy / dx of y = cos x x Just do the same cos x x = e x ln(cos(x))Or, you can do it a bit differently y = cos x x Take the logarithm of both sides gives ln y = x ln(cos x) Then you can differentiate both sides with respect to x, and see what you getStart your free trial In partnership with You are being redirected to Course Hero I want to submit the same problem to Course Hero CancelIf `y=e^(x) log (sin 2x),` find `(dy)/(dx)`
23 Derivative Find Dy By Dx Of Y Log X Cos X Youtube
Take Natural Logarithms of both sides lny = (lnx)2 Differentiate Implicitly, and apply the chain rule 1 y ⋅ dy dx = 2(lnx) ⋅ ( 1 x) Which we can rearrange to get dy dx = 2ylnx x = 2eln2xlnx x So then, when x = e we have dy dx = 2eln2elne eThe chain rule is a method for determining the derivative of a function based on its dependent variables If z is a function of y and y is a function of x, then the derivative of z with respect to x can be written \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx}To apply the Chain Rule, set u 1 u 1 as sin ( 2 x) sin ( 2 x) The derivative of ln ( u 1) ln ( u 1) with respect to u 1 u 1 is 1 u 1 1 u 1 Replace all occurrences of u 1 u 1 with sin ( 2 x) sin ( 2 x) Convert from 1 sin(2x) 1 sin ( 2 x) to csc(2x) csc ( 2 x)
Get The Solution To The Differential Equation Cos Y Sin2x Dx Cos 2y Cos 2x Dy 0 Mathematics Stack Exchange
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