Answer to Question #188363 in Calculus for Maureen

Question #188363

use the technique of derivative to find dy/dx

y=3 sin^5 x


1
Expert's answer
2021-05-07T12:02:22-0400

In this case, we use the Chain Rule.



y=3sin5x=3(sinx)5y=3\sin^5 x = 3(\sin x)^5


Let u=sinxu=\sin x so that y=3u5y=3u^5


Taking derivative of uu with respect to xx , we have:


dudx=cosx\frac{du}{dx} = \cos x


Similarly, the derivative of yy with respect to uu is given as


dydu=15u4\frac{dy}{du} = 15u^4


By Chain Rule,

dydx=dydu×dudx\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}

Therefore, dydx=15(sinx)4cosx\frac{dy}{dx} = 15(\sin x)^4 \cos x


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